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|00000000| 44 45 52 49 56 45 20 66 | 6f 72 20 57 69 6e 64 6f |DERIVE f|or Windo|
|00000010| 77 73 20 76 65 72 73 69 | 6f 6e 20 35 2e 30 33 20 |ws versi|on 5.03 |
|00000020| 44 66 57 20 66 69 6c 65 | 20 73 61 76 65 64 20 6f |DfW file| saved o|
|00000030| 6e 20 30 38 20 4d 61 72 | 20 32 30 30 31 0d 0a 1a |n 08 Mar| 2001...|
|00000040| 37 00 00 00 43 4f 4e 54 | 49 4e 55 45 44 5f 46 52 |7...CONT|INUED_FR|
|00000050| 41 43 54 49 4f 4e 28 75 | 2c 20 6e 29 3a 3d 46 4c |ACTION(u|, n):=FL|
|00000060| 4f 4f 52 28 49 54 45 52 | 41 54 45 53 28 31 2f 4d |OOR(ITER|ATES(1/M|
|00000070| 4f 44 28 78 5f 29 2c 20 | 78 5f 2c 20 75 2c 20 6e |OD(x_), |x_, u, n|
|00000080| 29 29 0d 0a 43 4f 4e 56 | 45 52 47 45 4e 54 28 78 |))..CONV|ERGENT(x|
|00000090| 2c 20 6b 2c 20 61 5f 2c | 20 62 5f 20 3a 3d 20 31 |, k, a_,| b_ := 1|
|000000a0| 2c 20 63 5f 20 3a 3d 20 | 31 2c 20 64 5f 20 3a 3d |, c_ := |1, d_ :=|
|000000b0| 20 30 2c 20 65 5f 2c 20 | 74 5f 29 3a 3d 50 52 4f | 0, e_, |t_):=PRO|
|000000c0| 47 28 61 5f 20 3a 3d 20 | 46 4c 4f 4f 52 28 78 29 |G(a_ := |FLOOR(x)|
|000000d0| 2c 20 65 5f 20 3a 3d 20 | 31 2f 4d 4f 44 28 78 29 |, e_ := |1/MOD(x)|
|000000e0| 2c 20 4c 4f 4f 50 28 49 | 46 28 6b 20 3d 20 30 2c |, LOOP(I|F(k = 0,|
|000000f0| 20 52 45 54 55 52 4e 20 | 61 5f 2f 63 5f 29 2c 20 | RETURN |a_/c_), |
|00000100| 74 5f 20 3a 3d 20 61 5f | 2c 20 61 5f 20 3a 3d 20 |t_ := a_|, a_ := |
|00000110| 46 4c 4f 4f 52 28 65 5f | 29 b7 61 5f 20 2b 20 62 |FLOOR(e_|).a_ + b|
|00000120| 5f 2c 20 62 5f 20 3a 3d | 20 74 5f 2c 20 74 5f 20 |_, b_ :=| t_, t_ |
|00000130| 3a 3d 20 63 5f 2c 20 63 | 5f 20 3a 3d 20 46 4c 4f |:= c_, c|_ := FLO|
|00000140| 4f 52 28 65 5f 29 b7 63 | 5f 20 2b 20 64 5f 2c 20 |OR(e_).c|_ + d_, |
|00000150| 64 5f 20 3a 3d 20 74 5f | 2c 20 65 5f 20 3a 3d 20 |d_ := t_|, e_ := |
|00000160| 31 2f 4d 4f 44 28 65 5f | 29 2c 20 6b 20 3a 2d 20 |1/MOD(e_|), k :- |
|00000170| 31 29 29 0d 0a 43 4f 4e | 56 45 52 47 45 4e 54 53 |1))..CON|VERGENTS|
|00000180| 28 78 2c 20 6b 2c 20 61 | 5f 2c 20 62 5f 20 3a 3d |(x, k, a|_, b_ :=|
|00000190| 20 31 2c 20 63 5f 20 3a | 3d 20 31 2c 20 64 5f 20 | 1, c_ :|= 1, d_ |
|000001a0| 3a 3d 20 30 2c 20 65 5f | 2c 20 6c 5f 2c 20 74 5f |:= 0, e_|, l_, t_|
|000001b0| 29 3a 3d 50 52 4f 47 28 | 61 5f 20 3a 3d 20 46 4c |):=PROG(|a_ := FL|
|000001c0| 4f 4f 52 28 78 29 2c 20 | 65 5f 20 3a 3d 20 31 2f |OOR(x), |e_ := 1/|
|000001d0| 4d 4f 44 28 78 29 2c 20 | 6c 5f 20 3a 3d 20 5b 61 |MOD(x), |l_ := [a|
|000001e0| 5f 5d 2c 20 4c 4f 4f 50 | 28 49 46 28 6b 20 3d 20 |_], LOOP|(IF(k = |
|000001f0| 30 2c 20 52 45 54 55 52 | 4e 20 6c 5f 29 2c 20 74 |0, RETUR|N l_), t|
|00000200| 5f 20 3a 3d 20 61 5f 2c | 20 61 5f 20 3a 3d 20 46 |_ := a_,| a_ := F|
|00000210| 4c 4f 4f 52 28 65 5f 29 | b7 61 5f 20 2b 20 62 5f |LOOR(e_)|.a_ + b_|
|00000220| 2c 20 62 5f 20 3a 3d 20 | 74 5f 2c 20 74 5f 20 3a |, b_ := |t_, t_ :|
|00000230| 3d 20 63 5f 2c 20 63 5f | 20 3a 3d 20 46 4c 4f 4f |= c_, c_| := FLOO|
|00000240| 52 28 65 5f 29 b7 63 5f | 20 2b 20 64 5f 2c 20 64 |R(e_).c_| + d_, d|
|00000250| 5f 20 3a 3d 20 74 5f 2c | 20 65 5f 20 3a 3d 20 31 |_ := t_,| e_ := 1|
|00000260| 2f 4d 4f 44 28 65 5f 29 | 2c 20 6b 20 3a 2d 20 31 |/MOD(e_)|, k :- 1|
|00000270| 2c 20 6c 5f 20 3a 3d 20 | 49 4e 53 45 52 54 28 61 |, l_ := |INSERT(a|
|00000280| 5f 2f 63 5f 2c 20 6c 5f | 2c 20 30 29 29 29 0d 0a |_/c_, l_|, 0)))..|
|00000290| 43 52 54 28 61 2c 20 6d | 2c 20 6d 5f 20 3a 3d 20 |CRT(a, m|, m_ := |
|000002a0| 31 2c 20 78 5f 20 3a 3d | 20 30 29 3a 3d 4c 4f 4f |1, x_ :=| 0):=LOO|
|000002b0| 50 28 49 46 28 6d 20 3d | 20 5b 5d 2c 20 52 45 54 |P(IF(m =| [], RET|
|000002c0| 55 52 4e 20 78 5f 29 2c | 20 78 5f 20 3a 3d 20 78 |URN x_),| x_ := x|
|000002d0| 5f 20 2b 20 28 46 49 52 | 53 54 28 61 29 20 2d 20 |_ + (FIR|ST(a) - |
|000002e0| 78 5f 29 b7 6d 5f b7 49 | 4e 56 45 52 53 45 5f 4d |x_).m_.I|NVERSE_M|
|000002f0| 4f 44 28 6d 5f 2c 20 46 | 49 52 53 54 28 6d 29 29 |OD(m_, F|IRST(m))|
|00000300| 2c 20 6d 5f 20 3a 2a 20 | 46 49 52 53 54 28 6d 29 |, m_ :* |FIRST(m)|
|00000310| 2c 20 78 5f 20 3a 3d 20 | 4d 4f 44 28 78 5f 2c 20 |, x_ := |MOD(x_, |
|00000320| 6d 5f 29 2c 20 61 20 3a | 3d 20 52 45 53 54 28 61 |m_), a :|= REST(a|
|00000330| 29 2c 20 6d 20 3a 3d 20 | 52 45 53 54 28 6d 29 29 |), m := |REST(m))|
|00000340| 0d 0a 43 59 43 4c 4f 54 | 4f 4d 49 43 28 6e 2c 20 |..CYCLOT|OMIC(n, |
|00000350| 78 29 3a 3d a3 28 28 78 | 5e 28 6e 2f 64 5f 29 20 |x):=.((x|^(n/d_) |
|00000360| 2d 20 31 29 5e 4d 4f 45 | 42 49 55 53 5f 4d 55 28 |- 1)^MOE|BIUS_MU(|
|00000370| 64 5f 29 2c 20 64 5f 2c | 20 44 49 56 49 53 4f 52 |d_), d_,| DIVISOR|
|00000380| 53 28 6e 29 29 0d 0a 44 | 49 56 49 53 4f 52 53 28 |S(n))..D|IVISORS(|
|00000390| 6e 29 3a 3d 53 4f 52 54 | 28 56 45 43 54 4f 52 28 |n):=SORT|(VECTOR(|
|000003a0| a3 28 75 5f 29 2c 20 75 | 5f 2c 20 7b 5b 31 5d 7d |.(u_), u|_, {[1]}|
|000003b0| b7 a3 28 56 45 43 54 4f | 52 28 4d 41 50 5f 4c 49 |..(VECTO|R(MAP_LI|
|000003c0| 53 54 28 5b 76 5f 99 31 | 5e 6b 5f 5d 2c 20 6b 5f |ST([v_.1|^k_], k_|
|000003d0| 2c 20 7b 30 2c 20 2e 2e | 2e 2c 20 76 5f 99 32 7d |, {0, ..|., v_.2}|
|000003e0| 29 2c 20 76 5f 2c 20 46 | 41 43 54 4f 52 53 28 6e |), v_, F|ACTORS(n|
|000003f0| 29 29 29 29 29 0d 0a 44 | 49 56 49 53 4f 52 5f 53 |)))))..D|IVISOR_S|
|00000400| 49 47 4d 41 28 6b 2c 20 | 6e 29 3a 3d a3 28 a4 28 |IGMA(k, |n):=.(.(|
|00000410| 76 5f 99 31 5e 28 6b b7 | 6a 5f 29 2c 20 6a 5f 2c |v_.1^(k.|j_), j_,|
|00000420| 20 30 2c 20 76 5f 99 32 | 29 2c 20 76 5f 2c 20 46 | 0, v_.2|), v_, F|
|00000430| 41 43 54 4f 52 53 28 6e | 29 29 0d 0a 44 49 56 49 |ACTORS(n|))..DIVI|
|00000440| 53 4f 52 5f 54 41 55 28 | 6e 29 3a 3d a3 28 76 5f |SOR_TAU(|n):=.(v_|
|00000450| 99 32 20 2b 20 31 2c 20 | 76 5f 2c 20 46 41 43 54 |.2 + 1, |v_, FACT|
|00000460| 4f 52 53 28 6e 29 29 0d | 0a 45 55 4c 45 52 5f 50 |ORS(n)).|.EULER_P|
|00000470| 48 49 28 6e 29 3a 3d 6e | b7 a3 28 31 20 2d 20 31 |HI(n):=n|..(1 - 1|
|00000480| 2f 76 5f 99 31 2c 20 76 | 5f 2c 20 46 41 43 54 4f |/v_.1, v|_, FACTO|
|00000490| 52 53 28 6e 29 29 0d 0a | 45 58 54 45 4e 44 45 44 |RS(n))..|EXTENDED|
|000004a0| 5f 47 43 44 28 61 2c 20 | 62 2c 20 71 5f 2c 20 72 |_GCD(a, |b, q_, r|
|000004b0| 5f 29 3a 3d 50 52 4f 47 | 28 61 20 3a 3d 20 5b 61 |_):=PROG|(a := [a|
|000004c0| 2c 20 5b 31 2c 20 30 5d | 5d 2c 20 62 20 3a 3d 20 |, [1, 0]|], b := |
|000004d0| 5b 62 2c 20 5b 30 2c 20 | 31 5d 5d 2c 20 4c 4f 4f |[b, [0, |1]], LOO|
|000004e0| 50 28 49 46 28 46 49 52 | 53 54 28 62 29 20 3d 20 |P(IF(FIR|ST(b) = |
|000004f0| 30 2c 20 65 78 69 74 29 | 2c 20 71 5f 20 3a 3d 20 |0, exit)|, q_ := |
|00000500| 46 49 52 53 54 28 61 29 | 2f 46 49 52 53 54 28 62 |FIRST(a)|/FIRST(b|
|00000510| 29 2c 20 71 5f 20 3a 3d | 20 52 4f 55 4e 44 28 52 |), q_ :=| ROUND(R|
|00000520| 45 28 71 5f 29 29 20 2b | 20 52 4f 55 4e 44 28 49 |E(q_)) +| ROUND(I|
|00000530| 4d 28 71 5f 29 29 b7 ee | 2c 20 72 5f 20 3a 3d 20 |M(q_))..|, r_ := |
|00000540| 61 20 2d 20 71 5f b7 62 | 2c 20 61 20 3a 3d 20 62 |a - q_.b|, a := b|
|00000550| 2c 20 62 20 3a 3d 20 72 | 5f 29 2c 20 49 46 28 46 |, b := r|_), IF(F|
|00000560| 49 52 53 54 28 61 29 20 | 3d 20 30 2c 20 52 45 54 |IRST(a) |= 0, RET|
|00000570| 55 52 4e 20 5b 30 2c 20 | 5b 30 2c 20 30 5d 5d 29 |URN [0, |[0, 0]])|
|00000580| 2c 20 4c 4f 4f 50 28 49 | 46 28 30 20 93 20 50 48 |, LOOP(I|F(0 . PH|
|00000590| 41 53 45 28 46 49 52 53 | 54 28 61 29 29 20 3c 20 |ASE(FIRS|T(a)) < |
|000005a0| b9 2f 32 2c 20 52 45 54 | 55 52 4e 20 61 29 2c 20 |./2, RET|URN a), |
|000005b0| 61 20 3a 2a 20 ee 29 29 | 0d 0a 46 41 52 45 59 28 |a :* .))|..FAREY(|
|000005c0| 6e 2c 20 61 5f 20 3a 3d | 20 31 2c 20 62 5f 20 3a |n, a_ :=| 1, b_ :|
|000005d0| 3d 20 31 2c 20 6c 5f 20 | 3a 3d 20 5b 31 5d 29 3a |= 1, l_ |:= [1]):|
|000005e0| 3d 4c 4f 4f 50 28 49 46 | 28 61 5f 20 3d 20 62 5f |=LOOP(IF|(a_ = b_|
|000005f0| 2c 20 49 46 28 62 5f 20 | 3d 20 6e 2c 20 52 45 54 |, IF(b_ |= n, RET|
|00000600| 55 52 4e 20 53 4f 52 54 | 28 6c 5f 29 2c 20 5b 62 |URN SORT|(l_), [b|
|00000610| 5f 20 3a 2b 20 31 2c 20 | 61 5f 20 3a 3d 20 31 5d |_ :+ 1, |a_ := 1]|
|00000620| 29 29 2c 20 49 46 28 47 | 43 44 28 61 5f 2c 20 62 |)), IF(G|CD(a_, b|
|00000630| 5f 29 20 3d 20 31 2c 20 | 6c 5f 20 3a 3d 20 41 50 |_) = 1, |l_ := AP|
|00000640| 50 45 4e 44 28 6c 5f 2c | 20 5b 61 5f 2f 62 5f 5d |PEND(l_,| [a_/b_]|
|00000650| 29 29 2c 20 61 5f 20 3a | 2b 20 31 29 0d 0a 46 49 |)), a_ :|+ 1)..FI|
|00000660| 42 4f 4e 41 43 43 49 28 | 6e 29 3a 3d 47 45 4e 5f |BONACCI(|n):=GEN_|
|00000670| 4c 55 43 41 53 28 6e 2c | 20 31 2c 20 2d 31 2c 20 |LUCAS(n,| 1, -1, |
|00000680| 30 2c 20 31 29 0d 0a 47 | 45 4e 5f 4c 55 43 41 53 |0, 1)..G|EN_LUCAS|
|00000690| 28 6e 2c 20 70 2c 20 71 | 2c 20 6c 30 2c 20 6c 31 |(n, p, q|, l0, l1|
|000006a0| 29 3a 3d 28 5b 30 2c 20 | 31 3b 20 2d 71 2c 20 70 |):=([0, |1; -q, p|
|000006b0| 5d 5e 6e 20 95 20 5b 6c | 30 2c 20 6c 31 5d 29 99 |]^n . [l|0, l1]).|
|000006c0| 31 0d 0a 4a 41 43 4f 42 | 49 28 61 2c 20 62 2c 20 |1..JACOB|I(a, b, |
|000006d0| 73 5f 20 3a 3d 20 31 2c | 20 74 5f 29 3a 3d 50 52 |s_ := 1,| t_):=PR|
|000006e0| 4f 47 28 49 46 28 62 20 | 3c 20 30 20 90 20 4d 4f |OG(IF(b |< 0 . MO|
|000006f0| 44 28 62 2c 20 32 29 20 | 3d 20 30 2c 20 52 45 54 |D(b, 2) |= 0, RET|
|00000700| 55 52 4e 20 3f 29 2c 20 | 49 46 28 47 43 44 28 61 |URN ?), |IF(GCD(a|
|00000710| 2c 20 62 29 20 3e 20 31 | 2c 20 52 45 54 55 52 4e |, b) > 1|, RETURN|
|00000720| 20 30 29 2c 20 4c 4f 4f | 50 28 49 46 28 61 20 3d | 0), LOO|P(IF(a =|
|00000730| 20 31 20 90 20 62 20 3d | 20 31 2c 20 52 45 54 55 | 1 . b =| 1, RETU|
|00000740| 52 4e 20 73 5f 29 2c 20 | 61 20 3a 3d 20 4d 4f 44 |RN s_), |a := MOD|
|00000750| 53 28 61 2c 20 62 29 2c | 20 49 46 28 61 20 3c 20 |S(a, b),| IF(a < |
|00000760| 30 20 8f 20 4d 4f 44 28 | 62 2c 20 34 29 20 3d 20 |0 . MOD(|b, 4) = |
|00000770| 33 2c 20 73 5f 20 3a 3d | 20 2d 73 5f 29 2c 20 61 |3, s_ :=| -s_), a|
|00000780| 20 3a 3d 20 41 42 53 28 | 61 29 2c 20 74 5f 20 3a | := ABS(|a), t_ :|
|00000790| 3d 20 30 2c 20 4c 4f 4f | 50 28 49 46 28 4d 4f 44 |= 0, LOO|P(IF(MOD|
|000007a0| 28 61 2c 20 32 29 20 3d | 20 31 2c 20 65 78 69 74 |(a, 2) =| 1, exit|
|000007b0| 29 2c 20 74 5f 20 3a 2b | 20 31 2c 20 61 20 3a 2f |), t_ :+| 1, a :/|
|000007c0| 20 32 29 2c 20 49 46 28 | 4d 4f 44 28 74 5f 2c 20 | 2), IF(|MOD(t_, |
|000007d0| 32 29 20 3d 20 31 20 8f | 20 4d 4f 44 53 28 62 2c |2) = 1 .| MODS(b,|
|000007e0| 20 38 29 20 3d 20 b1 33 | 2c 20 73 5f 20 3a 3d 20 | 8) = .3|, s_ := |
|000007f0| 2d 73 5f 29 2c 20 74 5f | 20 3a 3d 20 61 2c 20 61 |-s_), t_| := a, a|
|00000800| 20 3a 3d 20 62 2c 20 62 | 20 3a 3d 20 74 5f 2c 20 | := b, b| := t_, |
|00000810| 49 46 28 4d 4f 44 28 61 | 2c 20 34 29 20 3d 20 33 |IF(MOD(a|, 4) = 3|
|00000820| 20 8f 20 4d 4f 44 28 62 | 2c 20 34 29 20 3d 20 33 | . MOD(b|, 4) = 3|
|00000830| 2c 20 73 5f 20 3a 3d 20 | 2d 73 5f 29 29 29 0d 0a |, s_ := |-s_)))..|
|00000840| 4c 55 43 41 53 28 6e 29 | 3a 3d 56 5f 4c 55 43 41 |LUCAS(n)|:=V_LUCA|
|00000850| 53 28 6e 2c 20 31 2c 20 | 2d 31 29 0d 0a 4c 55 43 |S(n, 1, |-1)..LUC|
|00000860| 41 53 5f 4c 45 48 4d 45 | 52 28 70 2c 20 6d 5f 29 |AS_LEHME|R(p, m_)|
|00000870| 3a 3d 50 52 4f 47 28 6d | 5f 20 3a 3d 20 32 5e 70 |:=PROG(m|_ := 2^p|
|00000880| 20 2d 20 31 2c 20 53 4f | 4c 56 45 28 49 54 45 52 | - 1, SO|LVE(ITER|
|00000890| 41 54 45 28 4d 4f 44 28 | 73 5f 5e 32 20 2d 20 32 |ATE(MOD(|s_^2 - 2|
|000008a0| 2c 20 6d 5f 29 2c 20 73 | 5f 2c 20 34 2c 20 70 20 |, m_), s|_, 4, p |
|000008b0| 2d 20 32 29 20 3d 20 30 | 29 29 0d 0a 4d 45 52 53 |- 2) = 0|))..MERS|
|000008c0| 45 4e 4e 45 28 6e 29 3a | 3d 32 5e 4d 45 52 53 45 |ENNE(n):|=2^MERSE|
|000008d0| 4e 4e 45 5f 44 45 47 52 | 45 45 28 6e 29 20 2d 20 |NNE_DEGR|EE(n) - |
|000008e0| 31 0d 0a 4d 45 52 53 45 | 4e 4e 45 5f 44 45 47 52 |1..MERSE|NNE_DEGR|
|000008f0| 45 45 28 6e 29 3a 3d 5b | 32 2c 20 33 2c 20 35 2c |EE(n):=[|2, 3, 5,|
|00000900| 20 37 2c 20 31 33 2c 20 | 31 37 2c 20 31 39 2c 20 | 7, 13, |17, 19, |
|00000910| 33 31 2c 20 36 31 2c 20 | 38 39 2c 20 31 30 37 2c |31, 61, |89, 107,|
|00000920| 20 31 32 37 2c 20 35 32 | 31 2c 20 36 30 37 2c 20 | 127, 52|1, 607, |
|00000930| 31 32 37 39 2c 20 32 32 | 30 33 2c 20 32 32 38 31 |1279, 22|03, 2281|
|00000940| 2c 20 33 32 31 37 2c 20 | 34 32 35 33 2c 20 34 34 |, 3217, |4253, 44|
|00000950| 32 33 2c 20 39 36 38 39 | 2c 20 39 39 34 31 2c 20 |23, 9689|, 9941, |
|00000960| 31 31 32 31 33 2c 20 31 | 39 39 33 37 2c 20 32 31 |11213, 1|9937, 21|
|00000970| 37 30 31 2c 20 32 33 32 | 30 39 2c 20 34 34 34 39 |701, 232|09, 4449|
|00000980| 37 2c 20 38 36 32 34 33 | 2c 20 31 31 30 35 30 33 |7, 86243|, 110503|
|00000990| 2c 20 31 33 32 30 34 39 | 2c 20 32 31 36 30 39 31 |, 132049|, 216091|
|000009a0| 2c 20 37 35 36 38 33 39 | 2c 20 38 35 39 34 33 33 |, 756839|, 859433|
|000009b0| 2c 20 31 32 35 37 37 38 | 37 2c 20 31 33 39 38 32 |, 125778|7, 13982|
|000009c0| 36 39 2c 20 32 39 37 36 | 32 32 31 2c 20 33 30 32 |69, 2976|221, 302|
|000009d0| 31 33 37 37 2c 20 36 39 | 37 32 35 39 33 5d 99 6e |1377, 69|72593].n|
|000009e0| 0d 0a 4d 45 52 53 45 4e | 4e 45 5f 4c 49 53 54 28 |..MERSEN|NE_LIST(|
|000009f0| 6e 29 3a 3d 49 54 45 52 | 41 54 45 53 28 4e 45 58 |n):=ITER|ATES(NEX|
|00000a00| 54 5f 4d 45 52 53 45 4e | 4e 45 5f 44 45 47 52 45 |T_MERSEN|NE_DEGRE|
|00000a10| 45 28 6e 5f 29 2c 20 6e | 5f 2c 20 32 2c 20 6e 20 |E(n_), n|_, 2, n |
|00000a20| 2d 20 31 29 0d 0a 4d 4f | 45 42 49 55 53 5f 4d 55 |- 1)..MO|EBIUS_MU|
|00000a30| 28 6e 29 3a 3d a3 28 2d | 20 4d 41 58 28 32 20 2d |(n):=.(-| MAX(2 -|
|00000a40| 20 76 5f 99 32 2c 20 30 | 29 2c 20 76 5f 2c 20 46 | v_.2, 0|), v_, F|
|00000a50| 41 43 54 4f 52 53 28 6e | 29 29 0d 0a 4e 45 58 54 |ACTORS(n|))..NEXT|
|00000a60| 5f 4d 45 52 53 45 4e 4e | 45 5f 44 45 47 52 45 45 |_MERSENN|E_DEGREE|
|00000a70| 28 6e 2c 20 70 5f 29 3a | 3d 49 46 28 6e 20 3c 20 |(n, p_):|=IF(n < |
|00000a80| 32 2c 20 32 2c 20 50 52 | 4f 47 28 70 5f 20 3a 3d |2, 2, PR|OG(p_ :=|
|00000a90| 20 4e 45 58 54 5f 50 52 | 49 4d 45 28 6e 29 2c 20 | NEXT_PR|IME(n), |
|00000aa0| 4c 4f 4f 50 28 49 46 28 | 4c 55 43 41 53 5f 4c 45 |LOOP(IF(|LUCAS_LE|
|00000ab0| 48 4d 45 52 28 70 5f 29 | 2c 20 52 45 54 55 52 4e |HMER(p_)|, RETURN|
|00000ac0| 20 70 5f 29 2c 20 70 5f | 20 3a 3d 20 4e 45 58 54 | p_), p_| := NEXT|
|00000ad0| 5f 50 52 49 4d 45 28 70 | 5f 29 29 29 29 0d 0a 4e |_PRIME(p|_))))..N|
|00000ae0| 54 48 5f 50 52 49 4d 45 | 28 6e 29 3a 3d 49 54 45 |TH_PRIME|(n):=ITE|
|00000af0| 52 41 54 45 28 4e 45 58 | 54 5f 50 52 49 4d 45 28 |RATE(NEX|T_PRIME(|
|00000b00| 6b 5f 29 2c 20 6b 5f 2c | 20 31 2c 20 6e 29 0d 0a |k_), k_,| 1, n)..|
|00000b10| 50 45 4c 4c 28 6e 29 3a | 3d 47 45 4e 5f 4c 55 43 |PELL(n):|=GEN_LUC|
|00000b20| 41 53 28 6e 2c 20 32 2c | 20 2d 31 2c 20 31 2c 20 |AS(n, 2,| -1, 1, |
|00000b30| 30 29 0d 0a 50 45 52 46 | 45 43 54 28 6e 29 3a 3d |0)..PERF|ECT(n):=|
|00000b40| 53 55 42 53 54 28 28 6d | 5f 20 2b 20 31 29 b7 6d |SUBST((m|_ + 1).m|
|00000b50| 5f 2f 32 2c 20 6d 5f 2c | 20 4d 45 52 53 45 4e 4e |_/2, m_,| MERSENN|
|00000b60| 45 28 6e 29 29 0d 0a 50 | 52 49 4d 45 50 49 28 78 |E(n))..P|RIMEPI(x|
|00000b70| 2c 20 64 20 3a 3d 20 31 | 2c 20 61 20 3a 3d 20 31 |, d := 1|, a := 1|
|00000b80| 29 3a 3d 49 46 28 64 20 | 3e 20 31 2c 20 a4 28 49 |):=IF(d |> 1, .(I|
|00000b90| 46 28 50 52 49 4d 45 28 | 64 b7 6e 5f 20 2b 20 61 |F(PRIME(|d.n_ + a|
|00000ba0| 29 29 2c 20 6e 5f 2c 20 | 30 2c 20 28 78 20 2d 20 |)), n_, |0, (x - |
|00000bb0| 61 29 2f 64 29 2c 20 50 | 52 49 4d 45 50 49 28 78 |a)/d), P|RIMEPI(x|
|00000bc0| 2c 20 36 2c 20 31 29 20 | 2b 20 50 52 49 4d 45 50 |, 6, 1) |+ PRIMEP|
|00000bd0| 49 28 78 2c 20 36 2c 20 | 35 29 20 2b 20 49 46 28 |I(x, 6, |5) + IF(|
|00000be0| 78 20 92 20 33 2c 20 32 | 2c 20 43 48 49 28 32 2c |x . 3, 2|, CHI(2,|
|00000bf0| 20 78 2c 20 33 2c 20 31 | 29 29 29 0d 0a 50 52 49 | x, 3, 1|)))..PRI|
|00000c00| 4d 45 5f 46 41 43 54 4f | 52 49 5a 41 54 49 4f 4e |ME_FACTO|RIZATION|
|00000c10| 28 6e 29 3a 3d 46 41 43 | 54 4f 52 53 28 6e 29 0d |(n):=FAC|TORS(n).|
|00000c20| 0a 50 52 49 4d 45 5f 50 | 4f 57 45 52 3f 28 6e 2c |.PRIME_P|OWER?(n,|
|00000c30| 20 6b 5f 20 3a 3d 20 31 | 2c 20 74 5f 20 3a 3d 20 | k_ := 1|, t_ := |
|00000c40| 32 29 3a 3d 4c 4f 4f 50 | 28 49 46 28 74 5f 20 3e |2):=LOOP|(IF(t_ >|
|00000c50| 20 6e 2c 20 52 45 54 55 | 52 4e 20 66 61 6c 73 65 | n, RETU|RN false|
|00000c60| 29 2c 20 49 46 28 50 52 | 49 4d 45 28 6e 5e 28 31 |), IF(PR|IME(n^(1|
|00000c70| 2f 6b 5f 29 29 2c 20 65 | 78 69 74 29 2c 20 6b 5f |/k_)), e|xit), k_|
|00000c80| 20 3a 2b 20 31 2c 20 74 | 5f 20 3a 2a 20 32 29 0d | :+ 1, t|_ :* 2).|
|00000c90| 0a 50 52 49 4d 49 54 49 | 56 45 5f 52 4f 4f 54 28 |.PRIMITI|VE_ROOT(|
|00000ca0| 6e 2c 20 61 5f 20 3a 3d | 20 32 2c 20 6e 5f 2c 20 |n, a_ :=| 2, n_, |
|00000cb0| 6c 5f 2c 20 70 5f 29 3a | 3d 49 46 28 6e 20 3c 20 |l_, p_):|=IF(n < |
|00000cc0| 35 2c 20 6e 20 2d 20 31 | 2c 20 49 46 28 4d 4f 44 |5, n - 1|, IF(MOD|
|00000cd0| 28 6e 2c 20 34 29 20 3e | 20 30 2c 20 49 46 28 50 |(n, 4) >| 0, IF(P|
|00000ce0| 52 49 4d 45 5f 50 4f 57 | 45 52 3f 28 6e 2f 28 32 |RIME_POW|ER?(n/(2|
|00000cf0| 20 2d 20 4d 4f 44 28 6e | 2c 20 32 29 29 29 2c 20 | - MOD(n|, 2))), |
|00000d00| 50 52 4f 47 28 6e 5f 20 | 3a 3d 20 45 55 4c 45 52 |PROG(n_ |:= EULER|
|00000d10| 5f 50 48 49 28 6e 29 2c | 20 6c 5f 20 3a 3d 20 28 |_PHI(n),| l_ := (|
|00000d20| 46 41 43 54 4f 52 53 28 | 6e 5f 29 29 99 99 31 2c |FACTORS(|n_))..1,|
|00000d30| 20 4c 4f 4f 50 28 49 46 | 28 47 43 44 28 61 5f 2c | LOOP(IF|(GCD(a_,|
|00000d40| 20 6e 29 20 3d 20 31 2c | 20 49 46 28 45 56 45 52 | n) = 1,| IF(EVER|
|00000d50| 59 28 4d 4f 44 28 61 5f | 5e 28 6e 5f 2f 70 5f 29 |Y(MOD(a_|^(n_/p_)|
|00000d60| 2c 20 6e 29 20 94 20 31 | 2c 20 70 5f 2c 20 6c 5f |, n) . 1|, p_, l_|
|00000d70| 29 2c 20 52 45 54 55 52 | 4e 20 61 5f 29 29 2c 20 |), RETUR|N a_)), |
|00000d80| 61 5f 20 3a 2b 20 31 29 | 29 29 29 29 0d 0a 53 4f |a_ :+ 1)|))))..SO|
|00000d90| 4c 56 45 5f 4d 4f 44 28 | 75 2c 20 78 2c 20 6d 2c |LVE_MOD(|u, x, m,|
|00000da0| 20 61 5f 2c 20 62 5f 2c | 20 64 5f 29 3a 3d 50 52 | a_, b_,| d_):=PR|
|00000db0| 4f 47 28 61 5f 20 3a 3d | 20 44 49 46 28 4c 48 53 |OG(a_ :=| DIF(LHS|
|00000dc0| 28 75 29 20 2d 20 52 48 | 53 28 75 29 2c 20 78 29 |(u) - RH|S(u), x)|
|00000dd0| 2c 20 62 5f 20 3a 3d 20 | 4c 49 4d 28 52 48 53 28 |, b_ := |LIM(RHS(|
|00000de0| 75 29 20 2d 20 4c 48 53 | 28 75 29 2c 20 78 2c 20 |u) - LHS|(u), x, |
|00000df0| 30 29 2c 20 64 5f 20 3a | 3d 20 47 43 44 28 61 5f |0), d_ :|= GCD(a_|
|00000e00| 2c 20 6d 29 2c 20 49 46 | 28 4d 4f 44 28 62 5f 2c |, m), IF|(MOD(b_,|
|00000e10| 20 64 5f 29 20 94 20 30 | 2c 20 52 45 54 55 52 4e | d_) . 0|, RETURN|
|00000e20| 20 5b 5d 29 2c 20 6d 20 | 3a 3d 20 6d 2f 64 5f 2c | []), m |:= m/d_,|
|00000e30| 20 56 45 43 54 4f 52 28 | 4d 4f 44 28 62 5f 2f 64 | VECTOR(|MOD(b_/d|
|00000e40| 5f b7 49 4e 56 45 52 53 | 45 5f 4d 4f 44 28 61 5f |_.INVERS|E_MOD(a_|
|00000e50| 2f 64 5f 2c 20 6d 29 2c | 20 6d 29 20 2b 20 6b 5f |/d_, m),| m) + k_|
|00000e60| b7 6d 2c 20 6b 5f 2c 20 | 30 2c 20 64 5f 20 2d 20 |.m, k_, |0, d_ - |
|00000e70| 31 29 29 0d 0a 53 51 55 | 41 52 45 46 52 45 45 28 |1))..SQU|AREFREE(|
|00000e80| 6e 29 3a 3d 45 56 45 52 | 59 28 76 5f 99 32 20 3d |n):=EVER|Y(v_.2 =|
|00000e90| 20 31 2c 20 76 5f 2c 20 | 46 41 43 54 4f 52 53 28 | 1, v_, |FACTORS(|
|00000ea0| 6e 29 29 0d 0a 53 51 55 | 41 52 45 5f 52 4f 4f 54 |n))..SQU|ARE_ROOT|
|00000eb0| 28 61 2c 20 70 2c 20 61 | 5f 20 3a 3d 20 32 2c 20 |(a, p, a|_ := 2, |
|00000ec0| 62 5f 2c 20 73 5f 20 3a | 3d 20 2d 32 2c 20 74 5f |b_, s_ :|= -2, t_|
|00000ed0| 29 3a 3d 50 52 4f 47 28 | 49 46 28 70 20 3d 20 32 |):=PROG(|IF(p = 2|
|00000ee0| 20 90 20 4d 4f 44 28 61 | 2c 20 70 29 20 3d 20 30 | . MOD(a|, p) = 0|
|00000ef0| 2c 20 52 45 54 55 52 4e | 20 4d 4f 44 28 61 2c 20 |, RETURN| MOD(a, |
|00000f00| 70 29 29 2c 20 49 46 28 | 4a 41 43 4f 42 49 28 61 |p)), IF(|JACOBI(a|
|00000f10| 2c 20 70 29 20 3d 20 2d | 31 2c 20 52 45 54 55 52 |, p) = -|1, RETUR|
|00000f20| 4e 20 3f 29 2c 20 49 46 | 28 4d 4f 44 28 70 2c 20 |N ?), IF|(MOD(p, |
|00000f30| 34 29 20 3d 20 33 2c 20 | 52 45 54 55 52 4e 20 4d |4) = 3, |RETURN M|
|00000f40| 4f 44 28 61 5e 28 28 70 | 20 2b 20 31 29 2f 34 29 |OD(a^((p| + 1)/4)|
|00000f50| 2c 20 70 29 29 2c 20 49 | 46 28 4d 4f 44 28 70 2c |, p)), I|F(MOD(p,|
|00000f60| 20 38 29 20 3d 20 35 2c | 20 49 46 28 4d 4f 44 53 | 8) = 5,| IF(MODS|
|00000f70| 28 61 5e 28 28 70 20 2d | 20 31 29 2f 34 29 2c 20 |(a^((p -| 1)/4), |
|00000f80| 70 29 20 3d 20 31 2c 20 | 52 45 54 55 52 4e 20 4d |p) = 1, |RETURN M|
|00000f90| 4f 44 28 61 5e 28 28 70 | 20 2b 20 33 29 2f 38 29 |OD(a^((p| + 3)/8)|
|00000fa0| 2c 20 70 29 2c 20 52 45 | 54 55 52 4e 20 4d 4f 44 |, p), RE|TURN MOD|
|00000fb0| 28 32 b7 61 b7 4d 4f 44 | 28 28 34 b7 61 29 5e 28 |(2.a.MOD|((4.a)^(|
|00000fc0| 28 70 20 2d 20 35 29 2f | 38 29 2c 20 70 29 2c 20 |(p - 5)/|8), p), |
|00000fd0| 70 29 29 29 2c 20 4c 4f | 4f 50 28 49 46 28 4a 41 |p))), LO|OP(IF(JA|
|00000fe0| 43 4f 42 49 28 61 5f 2c | 20 70 29 20 3d 20 2d 31 |COBI(a_,| p) = -1|
|00000ff0| 2c 20 65 78 69 74 29 2c | 20 61 5f 20 3a 2b 20 31 |, exit),| a_ :+ 1|
|00001000| 29 2c 20 74 5f 20 3a 3d | 20 70 20 2d 20 31 2c 20 |), t_ :=| p - 1, |
|00001010| 4c 4f 4f 50 28 73 5f 20 | 3a 2b 20 31 2c 20 74 5f |LOOP(s_ |:+ 1, t_|
|00001020| 20 3a 2f 20 32 2c 20 49 | 46 28 4d 4f 44 28 74 5f | :/ 2, I|F(MOD(t_|
|00001030| 2c 20 32 29 20 3d 20 31 | 2c 20 65 78 69 74 29 29 |, 2) = 1|, exit))|
|00001040| 2c 20 61 5f 20 3a 3d 20 | 4d 4f 44 28 61 5f 5e 74 |, a_ := |MOD(a_^t|
|00001050| 5f 2c 20 70 29 2c 20 62 | 5f 20 3a 3d 20 4d 4f 44 |_, p), b|_ := MOD|
|00001060| 28 61 5e 28 28 74 5f 20 | 2b 20 31 29 2f 32 29 2c |(a^((t_ |+ 1)/2),|
|00001070| 20 70 29 2c 20 74 5f 20 | 3a 3d 20 49 4e 56 45 52 | p), t_ |:= INVER|
|00001080| 53 45 5f 4d 4f 44 28 61 | 2c 20 70 29 2c 20 4c 4f |SE_MOD(a|, p), LO|
|00001090| 4f 50 28 49 46 28 73 5f | 20 3c 20 30 2c 20 52 45 |OP(IF(s_| < 0, RE|
|000010a0| 54 55 52 4e 20 62 5f 29 | 2c 20 49 46 28 4d 4f 44 |TURN b_)|, IF(MOD|
|000010b0| 53 28 28 62 5f 5e 32 b7 | 74 5f 29 5e 32 5e 73 5f |S((b_^2.|t_)^2^s_|
|000010c0| 2c 20 70 29 20 3d 20 2d | 31 2c 20 62 5f 20 3a 3d |, p) = -|1, b_ :=|
|000010d0| 20 4d 4f 44 28 61 5f b7 | 62 5f 2c 20 70 29 29 2c | MOD(a_.|b_, p)),|
|000010e0| 20 61 5f 20 3a 3d 20 4d | 4f 44 28 61 5f 5e 32 2c | a_ := M|OD(a_^2,|
|000010f0| 20 70 29 2c 20 73 5f 20 | 3a 2d 20 31 29 29 0d 0a | p), s_ |:- 1))..|
|00001100| 55 5f 4c 55 43 41 53 28 | 6e 2c 20 70 2c 20 71 29 |U_LUCAS(|n, p, q)|
|00001110| 3a 3d 47 45 4e 5f 4c 55 | 43 41 53 28 6e 2c 20 70 |:=GEN_LU|CAS(n, p|
|00001120| 2c 20 71 2c 20 30 2c 20 | 31 29 0d 0a 55 5f 4d 4f |, q, 0, |1)..U_MO|
|00001130| 44 28 6e 2c 20 70 2c 20 | 71 2c 20 6d 2c 20 6c 5f |D(n, p, |q, m, l_|
|00001140| 2c 20 6c 6c 5f 2c 20 71 | 5f 20 3a 3d 20 31 29 3a |, ll_, q|_ := 1):|
|00001150| 3d 50 52 4f 47 28 6d 20 | 3a 3d 20 49 46 28 6d 20 |=PROG(m |:= IF(m |
|00001160| 3e 20 30 2c 20 6d 2c 20 | 30 2c 20 30 29 2c 20 6c |> 0, m, |0, 0), l|
|00001170| 5f 20 3a 3d 20 4d 4f 44 | 28 32 2c 20 6d 29 2c 20 |_ := MOD|(2, m), |
|00001180| 6c 6c 5f 20 3a 3d 20 70 | 2c 20 4f 75 74 70 75 74 |ll_ := p|, Output|
|00001190| 42 61 73 65 20 3a 3d 20 | 42 69 6e 61 72 79 2c 20 |Base := |Binary, |
|000011a0| 6e 20 3a 3d 20 4e 41 4d | 45 5f 54 4f 5f 43 4f 44 |n := NAM|E_TO_COD|
|000011b0| 45 53 28 53 54 52 49 4e | 47 28 6e 29 29 2c 20 4f |ES(STRIN|G(n)), O|
|000011c0| 75 74 70 75 74 42 61 73 | 65 20 3a 3d 20 44 65 63 |utputBas|e := Dec|
|000011d0| 69 6d 61 6c 2c 20 4c 4f | 4f 50 28 49 46 28 6e 20 |imal, LO|OP(IF(n |
|000011e0| 3d 20 5b 5d 2c 20 65 78 | 69 74 29 2c 20 49 46 28 |= [], ex|it), IF(|
|000011f0| 46 49 52 53 54 28 6e 29 | 20 3d 20 34 38 2c 20 50 |FIRST(n)| = 48, P|
|00001200| 52 4f 47 28 6c 6c 5f 20 | 3a 3d 20 50 4f 4c 59 5f |ROG(ll_ |:= POLY_|
|00001210| 4d 4f 44 28 6c 5f b7 6c | 6c 5f 20 2d 20 70 b7 71 |MOD(l_.l|l_ - p.q|
|00001220| 5f 2c 20 6d 29 2c 20 6c | 5f 20 3a 3d 20 50 4f 4c |_, m), l|_ := POL|
|00001230| 59 5f 4d 4f 44 28 6c 5f | 5e 32 20 2d 20 32 b7 71 |Y_MOD(l_|^2 - 2.q|
|00001240| 5f 2c 20 6d 29 2c 20 71 | 5f 20 3a 3d 20 4d 4f 44 |_, m), q|_ := MOD|
|00001250| 28 71 5f 5e 32 2c 20 6d | 29 29 2c 20 50 52 4f 47 |(q_^2, m|)), PROG|
|00001260| 28 6c 5f 20 3a 3d 20 50 | 4f 4c 59 5f 4d 4f 44 28 |(l_ := P|OLY_MOD(|
|00001270| 6c 5f b7 6c 6c 5f 20 2d | 20 70 b7 71 5f 2c 20 6d |l_.ll_ -| p.q_, m|
|00001280| 29 2c 20 6c 6c 5f 20 3a | 3d 20 50 4f 4c 59 5f 4d |), ll_ :|= POLY_M|
|00001290| 4f 44 28 6c 6c 5f 5e 32 | 20 2d 20 32 b7 71 5f b7 |OD(ll_^2| - 2.q_.|
|000012a0| 71 2c 20 6d 29 2c 20 71 | 5f 20 3a 3d 20 4d 4f 44 |q, m), q|_ := MOD|
|000012b0| 28 71 b7 71 5f 5e 32 2c | 20 6d 29 29 29 2c 20 6e |(q.q_^2,| m))), n|
|000012c0| 20 3a 3d 20 52 45 53 54 | 28 6e 29 29 2c 20 4d 4f | := REST|(n)), MO|
|000012d0| 44 28 28 32 b7 6c 6c 5f | 20 2d 20 70 b7 6c 5f 29 |D((2.ll_| - p.l_)|
|000012e0| b7 49 4e 56 45 52 53 45 | 5f 4d 4f 44 28 70 5e 32 |.INVERSE|_MOD(p^2|
|000012f0| 20 2d 20 34 b7 71 2c 20 | 6d 29 2c 20 6d 29 29 0d | - 4.q, |m), m)).|
|00001300| 0a 56 5f 4c 55 43 41 53 | 28 6e 2c 20 70 2c 20 71 |.V_LUCAS|(n, p, q|
|00001310| 29 3a 3d 47 45 4e 5f 4c | 55 43 41 53 28 6e 2c 20 |):=GEN_L|UCAS(n, |
|00001320| 70 2c 20 71 2c 20 32 2c | 20 70 29 0d 0a 56 5f 4d |p, q, 2,| p)..V_M|
|00001330| 4f 44 28 6e 2c 20 70 2c | 20 71 2c 20 6d 2c 20 6c |OD(n, p,| q, m, l|
|00001340| 5f 2c 20 6c 6c 5f 2c 20 | 71 5f 20 3a 3d 20 31 29 |_, ll_, |q_ := 1)|
|00001350| 3a 3d 50 52 4f 47 28 6d | 20 3a 3d 20 49 46 28 6d |:=PROG(m| := IF(m|
|00001360| 20 3e 20 30 2c 20 6d 2c | 20 30 2c 20 30 29 2c 20 | > 0, m,| 0, 0), |
|00001370| 6c 5f 20 3a 3d 20 4d 4f | 44 28 32 2c 20 6d 29 2c |l_ := MO|D(2, m),|
|00001380| 20 6c 6c 5f 20 3a 3d 20 | 70 2c 20 4f 75 74 70 75 | ll_ := |p, Outpu|
|00001390| 74 42 61 73 65 20 3a 3d | 20 42 69 6e 61 72 79 2c |tBase :=| Binary,|
|000013a0| 20 6e 20 3a 3d 20 4e 41 | 4d 45 5f 54 4f 5f 43 4f | n := NA|ME_TO_CO|
|000013b0| 44 45 53 28 53 54 52 49 | 4e 47 28 6e 29 29 2c 20 |DES(STRI|NG(n)), |
|000013c0| 4f 75 74 70 75 74 42 61 | 73 65 20 3a 3d 20 44 65 |OutputBa|se := De|
|000013d0| 63 69 6d 61 6c 2c 20 4c | 4f 4f 50 28 49 46 28 6e |cimal, L|OOP(IF(n|
|000013e0| 20 3d 20 5b 5d 2c 20 52 | 45 54 55 52 4e 20 6c 5f | = [], R|ETURN l_|
|000013f0| 29 2c 20 49 46 28 46 49 | 52 53 54 28 6e 29 20 3d |), IF(FI|RST(n) =|
|00001400| 20 34 38 2c 20 50 52 4f | 47 28 6c 6c 5f 20 3a 3d | 48, PRO|G(ll_ :=|
|00001410| 20 50 4f 4c 59 5f 4d 4f | 44 28 6c 5f b7 6c 6c 5f | POLY_MO|D(l_.ll_|
|00001420| 20 2d 20 70 b7 71 5f 2c | 20 6d 29 2c 20 6c 5f 20 | - p.q_,| m), l_ |
|00001430| 3a 3d 20 50 4f 4c 59 5f | 4d 4f 44 28 6c 5f 5e 32 |:= POLY_|MOD(l_^2|
|00001440| 20 2d 20 32 b7 71 5f 2c | 20 6d 29 2c 20 71 5f 20 | - 2.q_,| m), q_ |
|00001450| 3a 3d 20 4d 4f 44 28 71 | 5f 5e 32 2c 20 6d 29 29 |:= MOD(q|_^2, m))|
|00001460| 2c 20 50 52 4f 47 28 6c | 5f 20 3a 3d 20 50 4f 4c |, PROG(l|_ := POL|
|00001470| 59 5f 4d 4f 44 28 6c 5f | b7 6c 6c 5f 20 2d 20 70 |Y_MOD(l_|.ll_ - p|
|00001480| b7 71 5f 2c 20 6d 29 2c | 20 6c 6c 5f 20 3a 3d 20 |.q_, m),| ll_ := |
|00001490| 50 4f 4c 59 5f 4d 4f 44 | 28 6c 6c 5f 5e 32 20 2d |POLY_MOD|(ll_^2 -|
|000014a0| 20 32 b7 71 5f b7 71 2c | 20 6d 29 2c 20 71 5f 20 | 2.q_.q,| m), q_ |
|000014b0| 3a 3d 20 4d 4f 44 28 71 | b7 71 5f 5e 32 2c 20 6d |:= MOD(q|.q_^2, m|
|000014c0| 29 29 29 2c 20 6e 20 3a | 3d 20 52 45 53 54 28 6e |))), n :|= REST(n|
|000014d0| 29 29 29 0d 0a 63 28 72 | 2c 20 75 29 3a 3d ea 5e |)))..c(r|, u):=.^|
|000014e0| 28 2d 20 72 5e 32 2f 75 | 29 b7 28 b9 b7 75 29 5e |(- r^2/u|).(..u)^|
|000014f0| 28 2d 20 33 2f 32 29 0d | 0a 61 5f 3a 3d 0d 0a 62 |(- 3/2).|.a_:=..b|
|00001500| 5f 3a 3d 0d 0a 63 5f 3a | 3d 0d 0a 64 5f 3a 3d 0d |_:=..c_:|=..d_:=.|
|00001510| 0a 65 5f 3a 3d 0d 0a 6b | 5f 3a 3d 0d 0a 6c 30 3a |.e_:=..k|_:=..l0:|
|00001520| 3d 0d 0a 6c 31 3a 3d 0d | 0a 6c 5f 3a 3d 0d 0a 6c |=..l1:=.|.l_:=..l|
|00001530| 6c 5f 3a 3d 0d 0a 6d 5f | 3a 3d 0d 0a 6e 5f 3a 3d |l_:=..m_|:=..n_:=|
|00001540| 0d 0a 70 5f 3a 3d 0d 0a | 71 5f 3a 3d 0d 0a 72 5f |..p_:=..|q_:=..r_|
|00001550| 3a 3d 0d 0a 73 5f 3a 3d | 0d 0a 74 5f 3a 3d 0d 0a |:=..s_:=|..t_:=..|
|00001560| 76 3a 3d 5b 32 34 36 38 | 37 30 36 35 38 33 36 34 |v:=[2468|70658364|
|00001570| 37 37 33 33 38 38 32 32 | 36 38 34 31 37 32 33 34 |77338822|68417234|
|00001580| 36 31 33 31 36 38 36 37 | 36 34 36 34 30 38 39 38 |61316867|64640898|
|00001590| 35 34 34 34 33 32 32 36 | 32 35 38 32 37 33 36 38 |54443226|25827368|
|000015a0| 39 36 34 32 32 33 34 31 | 36 36 36 30 34 38 34 32 |96422341|66604842|
|000015b0| 38 33 31 38 37 39 39 37 | 34 38 34 39 30 34 38 37 |83187997|48490487|
|000015c0| 34 36 30 34 33 31 34 2c | 20 31 35 33 39 35 33 32 |4604314,| 1539532|
|000015d0| 30 30 35 34 34 38 36 39 | 36 38 36 35 35 32 34 34 |00544869|68655244|
|000015e0| 32 31 34 36 36 34 36 35 | 33 33 34 33 36 39 36 37 |21466465|33436967|
|000015f0| 35 36 37 31 38 36 30 30 | 30 35 32 33 32 32 31 37 |56718600|05232217|
|00001600| 37 32 37 37 33 38 39 32 | 39 31 35 35 31 32 38 38 |72773892|91551288|
|00001610| 30 37 31 31 33 38 33 32 | 32 38 38 35 37 38 36 32 |07113832|28857862|
|00001620| 30 39 35 37 36 36 33 34 | 37 34 39 35 35 3b 20 32 |09576634|74955; 2|
|00001630| 34 34 38 37 39 33 37 34 | 37 33 35 36 30 32 38 35 |44879374|73560285|
|00001640| 37 35 39 39 38 30 30 32 | 34 37 31 30 38 31 39 38 |75998002|47108198|
|00001650| 38 30 37 32 32 31 37 38 | 37 31 31 33 32 35 33 33 |80722178|71132533|
|00001660| 36 30 38 36 39 33 39 34 | 36 34 38 33 36 33 38 39 |60869394|64836389|
|00001670| 34 35 39 38 38 39 30 30 | 31 32 31 39 30 39 34 31 |45988900|12190941|
|00001680| 34 32 32 38 35 31 32 33 | 33 37 35 32 39 35 30 36 |42285123|37529506|
|00001690| 35 2c 20 31 31 32 34 31 | 37 39 38 32 34 30 34 34 |5, 11241|79824044|
|000016a0| 36 39 31 39 31 38 36 37 | 31 34 38 38 33 36 32 36 |69191867|14883626|
|000016b0| 31 30 35 32 37 39 33 38 | 37 38 34 38 32 35 39 32 |10527938|78482592|
|000016c0| 30 31 39 31 32 31 30 36 | 30 33 37 31 35 32 35 34 |01912106|03715254|
|000016d0| 34 35 37 34 32 36 37 33 | 39 36 36 31 32 39 32 30 |45742673|96612920|
|000016e0| 34 31 33 32 36 33 30 38 | 37 34 34 36 32 30 33 39 |41326308|74462039|
|000016f0| 35 33 33 38 35 30 35 3b | 20 39 30 32 36 34 32 35 |5338505;| 9026425|
|00001700| 32 34 30 32 32 30 39 32 | 39 35 38 39 34 39 39 35 |24022092|95894995|
|00001710| 31 34 30 34 36 33 30 33 | 36 35 36 32 31 30 38 32 |14046303|65621082|
|00001720| 30 38 38 37 30 34 39 32 | 37 30 39 38 31 39 38 34 |08870492|70981984|
|00001730| 31 30 33 39 30 38 38 36 | 36 32 34 35 37 33 36 33 |10390886|62457363|
|00001740| 34 34 37 37 30 32 32 34 | 34 38 32 30 39 36 31 32 |44770224|48209612|
|00001750| 36 38 36 38 30 33 30 35 | 32 33 38 39 2c 20 35 33 |68680305|2389, 53|
|00001760| 30 30 39 38 30 30 34 30 | 31 35 31 37 36 30 33 30 |00980040|15176030|
|00001770| 34 37 38 30 35 36 33 30 | 34 36 35 39 35 36 30 34 |47805630|46595604|
|00001780| 34 39 36 36 34 33 38 33 | 37 35 30 34 32 36 30 38 |49664383|75042608|
|00001790| 34 36 30 32 34 38 35 34 | 39 36 35 31 36 33 35 36 |46024854|96516356|
|000017a0| 38 35 31 38 39 38 32 34 | 38 38 37 31 31 33 33 32 |85189824|88711332|
|000017b0| 34 30 32 37 36 37 35 31 | 31 31 30 32 33 36 37 30 |40276751|11023670|
|000017c0| 33 3b 20 34 38 38 35 37 | 39 37 34 34 30 31 39 31 |3; 48857|97440191|
|000017d0| 36 38 34 38 33 38 37 35 | 31 35 37 35 34 38 36 31 |68483875|15754861|
|000017e0| 39 32 30 34 37 37 30 31 | 38 37 39 35 30 38 33 37 |92047701|87950837|
|000017f0| 34 37 33 31 33 37 37 39 | 33 39 35 37 32 37 36 31 |47313779|39572761|
|00001800| 38 36 39 37 34 30 36 39 | 30 30 39 35 30 34 33 38 |86974069|00950438|
|00001810| 30 33 35 30 32 33 32 38 | 36 35 38 34 38 37 37 33 |03502328|65848773|
|00001820| 33 32 35 36 34 37 2c 20 | 31 35 34 33 35 39 34 35 |325647, |15435945|
|00001830| 39 35 37 35 38 36 32 38 | 37 36 34 30 37 38 36 36 |95758628|76407866|
|00001840| 32 34 31 33 32 39 33 39 | 30 38 34 39 33 36 38 31 |24132939|08493681|
|00001850| 34 37 34 34 31 30 33 37 | 31 34 31 30 35 38 33 32 |47441037|14105832|
|00001860| 34 38 36 36 33 34 34 34 | 32 37 36 32 37 36 31 33 |48663444|27627613|
|00001870| 34 39 32 34 30 38 39 35 | 30 33 35 35 30 39 34 35 |49240895|03550945|
|00001880| 36 37 39 30 30 35 30 32 | 39 36 35 37 3b 20 35 38 |67900502|9657; 58|
|00001890| 31 35 39 33 39 35 30 34 | 35 30 39 33 38 38 36 37 |15939504|50938867|
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|00002240| 32 20 45 58 54 45 4e 44 | 45 44 5f 47 43 44 28 61 |2 EXTEND|ED_GCD(a|
|00002250| 2c 20 62 29 20 73 69 6d | 70 6c 69 66 69 65 73 20 |, b) sim|plifies |
|00002260| 66 6f 72 20 69 6e 74 65 | 67 65 72 73 20 28 6f 72 |for inte|gers (or|
|00002270| 20 6d 6f 72 65 20 67 65 | 6e 65 72 61 6c 6c 79 20 | more ge|nerally |
|00002280| 47 61 75 73 73 69 61 6e | 20 69 6e 74 65 67 65 72 |Gaussian| integer|
|00002290| 73 2c 20 69 2e 65 2e 20 | 63 6f 6d 70 6c 65 78 20 |s, i.e. |complex |
|000022a0| 6e 75 6d 62 65 72 73 20 | 77 69 74 68 20 69 6e 74 |numbers |with int|
|000022b0| 65 67 65 72 20 63 6f 6f | 72 64 69 6e 61 74 65 73 |eger coo|rdinates|
|000022c0| 29 20 61 20 61 6e 64 20 | 62 20 74 6f 20 61 20 76 |) a and |b to a v|
|000022d0| 65 63 74 6f 72 20 5b 64 | 2c 20 5b 78 2c 20 79 5d |ector [d|, [x, y]|
|000022e0| 5d 20 6f 66 20 28 47 61 | 75 73 73 69 61 6e 29 20 |] of (Ga|ussian) |
|000022f0| 69 6e 74 65 67 65 72 73 | 20 73 75 63 68 20 74 68 |integers| such th|
|00002300| 61 74 0d 0a 5c 70 61 72 | 20 0d 0a 5c 70 61 72 20 |at..\par| ..\par |
|00002310| 5c 70 61 72 64 5c 71 63 | 5c 70 6c 61 69 6e 5c 6c |\pard\qc|\plain\l|
|00002320| 61 6e 67 31 30 33 33 5c | 66 34 5c 66 73 32 30 5c |ang1033\|f4\fs20\|
|00002330| 63 66 32 20 64 20 3d 20 | 67 63 64 28 61 2c 20 62 |cf2 d = |gcd(a, b|
|00002340| 29 20 3d 20 78 5c 70 6c | 61 69 6e 5c 66 34 5c 66 |) = x\pl|ain\f4\f|
|00002350| 73 32 30 5c 63 66 32 20 | 5c 27 62 37 5c 70 6c 61 |s20\cf2 |\'b7\pla|
|00002360| 69 6e 5c 6c 61 6e 67 31 | 30 33 33 5c 66 34 5c 66 |in\lang1|033\f4\f|
|00002370| 73 32 30 5c 63 66 32 20 | 61 20 2b 20 79 5c 70 6c |s20\cf2 |a + y\pl|
|00002380| 61 69 6e 5c 66 34 5c 66 | 73 32 30 5c 63 66 32 20 |ain\f4\f|s20\cf2 |
|00002390| 5c 27 62 37 5c 70 6c 61 | 69 6e 5c 6c 61 6e 67 31 |\'b7\pla|in\lang1|
|000023a0| 30 33 33 5c 66 34 5c 66 | 73 32 30 5c 63 66 32 20 |033\f4\f|s20\cf2 |
|000023b0| 62 0d 0a 5c 70 61 72 20 | 5c 70 61 72 64 5c 70 6c |b..\par |\pard\pl|
|000023c0| 61 69 6e 5c 6c 61 6e 67 | 31 30 33 33 5c 66 34 5c |ain\lang|1033\f4\|
|000023d0| 66 73 32 30 5c 63 66 32 | 20 0d 0a 5c 70 61 72 20 |fs20\cf2| ..\par |
|000023e0| 75 73 69 6e 67 20 74 68 | 65 20 65 78 74 65 6e 64 |using th|e extend|
|000023f0| 65 64 20 45 75 63 6c 69 | 64 65 61 6e 20 67 63 64 |ed Eucli|dean gcd|
|00002400| 20 61 6c 67 6f 72 69 74 | 68 6d 2e 20 20 46 6f 72 | algorit|hm.  For|
|00002410| 20 65 78 61 6d 70 6c 65 | 2c 20 74 6f 20 66 69 6e | example|, to fin|
|00002420| 64 20 74 68 65 20 65 78 | 74 65 6e 64 65 64 20 67 |d the ex|tended g|
|00002430| 63 64 20 6f 66 20 20 32 | 30 35 38 30 20 61 6e 64 |cd of  2|0580 and|
|00002440| 20 38 35 31 37 36 2c 20 | 73 69 6d 70 6c 69 66 79 | 85176, |simplify|
|00002450| 20 74 68 65 20 65 78 70 | 72 65 73 73 69 6f 6e 0d | the exp|ression.|
|00002460| 0a 5c 70 61 72 20 5c 70 | 6c 61 69 6e 5c 6c 61 6e |.\par \p|lain\lan|
|00002470| 67 31 30 33 33 5c 66 35 | 5c 66 73 32 30 20 0d 0a |g1033\f5|\fs20 ..|
|00002480| 5c 70 61 72 20 5c 70 61 | 72 64 5c 71 63 5c 70 6c |\par \pa|rd\qc\pl|
|00002490| 61 69 6e 5c 6c 61 6e 67 | 31 30 33 33 5c 66 35 5c |ain\lang|1033\f5\|
|000024a0| 66 73 32 30 5c 63 66 31 | 20 45 58 54 45 4e 44 45 |fs20\cf1| EXTENDE|
|000024b0| 44 5f 47 43 44 28 32 30 | 35 38 30 2c 38 35 31 37 |D_GCD(20|580,8517|
|000024c0| 36 29 0d 0a 5c 70 61 72 | 20 7d 0d 0a ff ff 00 00 |6)..\par| }......|
|000024d0| 08 00 43 45 78 70 6e 4f | 62 6a 38 00 00 00 28 01 |..CExpnO|bj8...(.|
|000024e0| 00 00 90 01 00 00 f4 01 | 00 00 00 04 55 73 65 72 |........|....User|
|000024f0| 00 00 00 00 00 00 f0 bf | 01 00 00 00 01 00 00 00 |........|........|
|00002500| f4 45 58 54 45 4e 44 45 | 44 5f 47 43 44 28 61 2c |.EXTENDE|D_GCD(a,|
|00002510| 62 2c 71 5f 2c 72 5f 29 | 3a 3d 50 52 4f 47 28 61 |b,q_,r_)|:=PROG(a|
|00002520| 3a 3d 5b 61 2c 5b 31 2c | 30 5d 5d 2c 62 3a 3d 5b |:=[a,[1,|0]],b:=[|
|00002530| 62 2c 5b 30 2c 31 5d 5d | 2c 4c 4f 4f 50 28 49 46 |b,[0,1]]|,LOOP(IF|
|00002540| 28 46 49 52 53 54 28 62 | 29 3d 30 2c 65 78 69 74 |(FIRST(b|)=0,exit|
|00002550| 29 2c 71 5f 3a 3d 46 49 | 52 53 54 28 61 29 2f 46 |),q_:=FI|RST(a)/F|
|00002560| 49 52 53 54 28 62 29 2c | 71 5f 3a 3d 52 4f 55 4e |IRST(b),|q_:=ROUN|
|00002570| 44 28 52 45 28 71 5f 29 | 29 2b 52 4f 55 4e 44 28 |D(RE(q_)|)+ROUND(|
|00002580| 49 4d 28 71 5f 29 29 2a | 23 69 2c 72 5f 3a 3d 61 |IM(q_))*|#i,r_:=a|
|00002590| 2d 71 5f 2a 62 2c 61 3a | 3d 62 2c 62 3a 3d 72 5f |-q_*b,a:|=b,b:=r_|
|000025a0| 29 2c 49 46 28 46 49 52 | 53 54 28 61 29 3d 30 2c |),IF(FIR|ST(a)=0,|
|000025b0| 52 45 54 55 52 4e 28 5b | 30 2c 5b 30 2c 30 5d 5d |RETURN([|0,[0,0]]|
|000025c0| 29 29 2c 4c 4f 4f 50 28 | 49 46 28 30 3c 3d 50 48 |)),LOOP(|IF(0<=PH|
|000025d0| 41 53 45 28 46 49 52 53 | 54 28 61 29 29 3c 70 69 |ASE(FIRS|T(a))<pi|
|000025e0| 2f 32 2c 52 45 54 55 52 | 4e 28 61 29 29 2c 61 3a |/2,RETUR|N(a)),a:|
|000025f0| 2a 23 69 29 29 01 80 08 | 00 00 00 00 02 00 00 e4 |*#i))...|........|
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+--------+-------------------------+-------------------------+--------+--------+