A096020 Number of Pythagorean quintuples mod n; i.e., number of solutions to v^2 + w^2 + x^2 + y^2 = z^2 mod n.

1, 16, 81, 192, 625, 1296, 2401, 3072, 6723, 10000, 14641, 15552, 28561, 38416, 50625, 47104, 83521, 107568, 130321, 120000, 194481, 234256, 279841, 248832, 393125, 456976, 544563, 460992, 707281, 810000, 923521, 753664

Offset

1,2

Links

Table of n, a(n) for n=1..32.

L. Toth, Counting Solutions of Quadratic Congruences in Several Variables Revisited, J. Int. Seq. 17 (2014) # 14.11.6.

Example

x + 16 x^2 + 81 x^3 + 192 x^4 + 625 x^5 + 1296 x^6 + 2401 x^7 + ...

Mathematica

Table[cnt=0; Do[If[Mod[v^2+w^2+x^2+y^2-z^2, n]==0, cnt++ ], {v, 0, n-1}, {w, 0, n-1}, {x, 0, n-1}, {y, 0, n-1}, {z, 0, n-1}]; cnt, {n, 30}]
a[ n_] := If[ n < 1, 0, Sum[ 1 - Sign[ Mod[ v^2 + w^2 + x^2 + y^2 - z^2, n]], {v, n}, {w, n}, {x, n}, {y, n}, {z, n}]]; (* Michael Somos, Jan 21 2012 *)

Crossrefs

Cf. A062775 (number of solutions to x^2 + y^2 = z^2 mod n), A096018 (number of solutions to w^2 + x^2 + y^2 = z^2 mod n).

Sequence in context: A295071 A223951 A041490 * A016898 A224135 A265154

Adjacent sequences: A096017 A096018 A096019 * A096021 A096022 A096023

Keyword

mult,nonn

Author

T. D. Noe, Jun 15 2004

Status

approved