A288099 Number of solutions to x^4 + y^4 = z^4 mod n.

1, 4, 9, 24, 33, 36, 49, 192, 99, 132, 121, 216, 97, 196, 297, 1536, 193, 396, 361, 792, 441, 484, 529, 1728, 925, 388, 1377, 1176, 1121, 1188, 961, 6144, 1089, 772, 1617, 2376, 1441, 1444, 873, 6336, 481, 1764, 1849, 2904, 3267, 2116, 2209, 13824, 2695, 3700, 1737

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), this sequence (k=4), A288100 (k=5), A288101 (k=6), A288102 (k=7), A288103 (k=8), A288104 (k=9), A288105 (k=10).

Programs

PARI

a(n)={my(p=Mod(sum(i=0, n-1, x^lift(Mod(i,n)^4)), 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