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

1,2

Links

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

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 *)

Prog

(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

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).

Sequence in context: A270461 A046422 A288099 * A286729 A159068 A255876

Adjacent sequences: A288100 A288101 A288102 * A288104 A288105 A288106

Keyword

nonn,mult

Author

Seiichi Manyama, Jun 05 2017

Extensions

Keyword:mult added by Andrew Howroyd, Jul 17 2018

Status

approved