VAL, спасибо. Давайте разбираться предметно.
Я свои программы приводил
здесь. В них есть ошибки?
Не знаю. Меня, например, смущает округление в задаче, где все изначально целочисленно.
Цитата:
И конечно предлагаю взглянуть на Ваши программы и на результаты их работы.
Пожалуйста.
Вот для 8 паттернов с 98 на 11-м месте (это maple, а не PARI):
Код:
restart; with(combinat); with(NumberTheory);
S := permute([17, 19, 23, 29, 31, 37]);
for ii from 31 by 90 to 720 do P := S[ii]; print(P); M := [P[1]^2, 2*P[2]^2, 3*P[3]^2, 2^2, 5*P[4]^2, 2*3^2, 7*13^2, 2^5, 3*11^2, 2*5^2, P[5]^2, 3*2^2, P[6]^2, 2*7^2, 5*3^2]; for i to 15 do m || i := M[i] end do; a := 2*P[2]^2; mm := 6*ilcm(op(M))/a; print(cat('a', " ="), a); print(cat('m', " ="), mm); r1 := rhs(op(msolve(a*x-1, m1))); r2 := rhs(op(msolve(a*x+1, (1/3)*m3))); r3 := rhs(op(msolve(a*x+3, (1/5)*m5))); r4 := rhs(op(msolve(a*x-5, 27))); r5 := rhs(op(msolve(a*x+5, (1/7)*m7))); r6 := rhs(op([msolve(a*x-26, 64)][1])); r7 := rhs(op(msolve(a*x+7, (1/3)*m9))); r8 := rhs(op(msolve(a*x+8, (1/2)*m10))); r9 := rhs(op(msolve(a*x+9, m11))); r10 := rhs(op(msolve(a*x+11, m13))); r11 := rhs(op(msolve(a*x+12, (1/2)*m14))); p1 := chrem([seq(r || i, i = 1 .. 11)], [m1, (1/3)*m3, (1/5)*m5, 27, (1/7)*m7, 64, (1/3)*m9, (1/2)*m10, m11, m13, (1/2)*m14]); print(cat('p1', " ="), p1); E := [[5, 10], [7, 14], [11, 9], [13, 7], [P[1], 1], [P[3], 3], [P[4], 5], [P[2], 2], [P[5], 11], [P[6], 13]]; W := []; for b in E do for j from 0 do q := (a*(j*mm+p1)+b[2]-2)/b[1]^2; if `mod`(q, b[1]) = 0 then break end if end do; W := [op(W), [b[1], j]] end do; print(sort(W)); print(M[3], M[5]); print(14000+ii); T := [seq(0, i = 1 .. 15)]; for i to 15 do for j from 100000000000 to 100000010000 do if tau(a*(j*mm+p1)+i-2) = 12 then T[i] := T[i]+1 end if end do end do; print(T); t := mul(s, s in T)/10.^60; print(t, 1/t); print() end do;
А вот вывод:
Код:
[17, 23, 29, 19, 31, 37]
a =, 1058
m =, 2498329881229038838581600
p1 =, 4490201041996487392891549
[[5, 3], [7, 0], [11, 5], [13, 10], [17, 14], [19, 16], [23, 11], [29, 11], [31, 21], [37, 19]]
2523, 1805
14031
[2302, 814, 773, 2347, 782, 776, 830, 800, 735, 659, 2321, 779, 2382, 694, 782]
-15 14
1.550787150 10 , 6.448338187 10
[19, 17, 23, 29, 31, 37]
a =, 578
m =, 4573067498858690469237600
p1 =, 7042158276307918213642189
[[5, 0], [7, 1], [11, 8], [13, 1], [17, 0], [19, 7], [23, 5], [29, 19], [31, 12], [37, 28]]
1587, 4205
14121
[2387, 781, 784, 2355, 826, 786, 761, 802, 734, 669, 2456, 827, 2413, 679, 775]
-15 14
1.727256731 10 , 5.789527301 10
[19, 31, 37, 17, 23, 29]
a =, 1922
m =, 1375251308189554157762400
p1 =, 706510592256678820525261
[[5, 2], [7, 5], [11, 2], [13, 11], [17, 12], [19, 6], [23, 16], [29, 16], [31, 19], [37, 3]]
4107, 1445
14211
[2376, 794, 827, 2396, 812, 775, 716, 713, 732, 625, 2319, 778, 2372, 673, 793]
-15 14
1.254856100 10 , 7.969041231 10
[23, 29, 31, 17, 19, 37]
a =, 1682
m =, 1571482172616125500130400
p1 =, 2950952235732722963586181
[[5, 1], [7, 1], [11, 8], [13, 1], [17, 7], [19, 11], [23, 11], [29, 4], [31, 13], [37, 34]]
2883, 1445
14301
[2378, 759, 840, 2340, 726, 785, 720, 791, 741, 655, 2310, 727, 2389, 666, 765]
-15 14
1.142409326 10 , 8.753429942 10
[29, 19, 23, 17, 31, 37]
a =, 722
m =, 3660987554487982120802400
p1 =, 23269416888858390477061
[[5, 4], [7, 2], [11, 1], [13, 3], [17, 0], [19, 5], [23, 0], [29, 16], [31, 23], [37, 6]]
1587, 1445
14391
[2364, 749, 791, 2405, 746, 876, 761, 760, 730, 644, 2458, 817, 2299, 700, 810]
-15 14
1.566739272 10 , 6.382682925 10
[31, 17, 19, 23, 29, 37]
a =, 578
m =, 4573067498858690469237600
p1 =, 950850093312928522906189
[[5, 0], [7, 2], [11, 4], [13, 3], [17, 12], [19, 2], [23, 21], [29, 16], [31, 2], [37, 8]]
1083, 2645
14481
[2378, 790, 806, 2358, 834, 780, 767, 763, 724, 646, 2366, 756, 2445, 690, 804]
-15 14
1.542374947 10 , 6.483507800 10
[31, 29, 37, 17, 19, 23]
a =, 1682
m =, 1571482172616125500130400
p1 =, 1435836264660139229331781
[[5, 2], [7, 0], [11, 2], [13, 7], [17, 8], [19, 4], [23, 13], [29, 16], [31, 24], [37, 18]]
4107, 1445
14571
[2438, 847, 766, 2451, 838, 779, 753, 810, 750, 640, 2385, 807, 2376, 672, 831]
-15 14
1.892215312 10 , 5.284810844 10
[37, 23, 29, 17, 19, 31]
a =, 1058
m =, 2498329881229038838581600
p1 =, 3911229542632454810083549
[[5, 3], [7, 3], [11, 3], [13, 6], [17, 6], [19, 1], [23, 6], [29, 28], [31, 26], [37, 1]]
2523, 1445
14661
[2405, 860, 806, 2366, 789, 807, 766, 795, 739, 602, 2336, 752, 2399, 724, 779]
-15 14
1.617140042 10 , 6.183756348 10
Для паттернов с 28 на 4-м месте программа аналогична. Только
Код:
M := [P[1]^2, 2*P[2]^2, 3*P[3]^2, 7*2^2, 5*P[4]^2, 2*3^2, 11^2, 2^5, 3*P[5]^2, 2*5^2, 7^2, 3*2^2, 13^2, 2*P[6]^2, 5*3^2]
А вот ее вывод
Код:
[2384, 789, 794, 814, 799, 793, 2201, 762, 793, 607, 2113, 792, 2299, 754, 766]
Действительно для 28 подходящих случаев больше (814 против примерно 700). Но далеко не в 8 раз.