A288103 Number of solutions to x^8 + y^8 = z^8 mod n.

1, 4, 9, 24, 33, 36, 49, 192, 99, 132, 121, 216, 97, 196, 297, 1536, 385, 396, 361, 792, 441, 484, 529, 1728, 925, 388, 1377, 1176, 1121, 1188, 961, 12288, 1089, 1540, 1617, 2376, 1441, 1444, 873, 6336, 641, 1764, 1849, 2904, 3267, 2116, 2209, 13824, 2695, 3700

Offset: 1

Author

Seiichi Manyama, Jun 05 2017

Keywords

• nonn
• mult

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Number of solutions to x^k + y^k = z^k mod n: A062775 (k=2), A063454 (k=3), A288099 (k=4), A288100 (k=5), A288101 (k=6), A288102 (k=7), this sequence (k=8), A288104 (k=9), A288105 (k=10).

Programs

Mathematica

Table[cnt=0; Do[If[Mod[x^8 + y^8 - z^8, n]==0, cnt++], {x, 0, n-1}, {y, 0, n-1}, {z, 0, n-1}]; cnt, {n, 50}] (* Vincenzo Librandi, Jul 18 2018 *)

PARI

a(n)={my(p=Mod(sum(i=0, n-1, x^lift(Mod(i,n)^8)), 1-x^n)); vecsum(Vec( serconvol(lift(p^2) + O(x^n), lift(p) + O(x^n))))} \\ Andrew Howroyd, Jul 17 2018

Extensions

Keyword:mult added by Andrew Howroyd, Jul 17 2018