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

Author

T. D. Noe, Jun 15 2004

Keywords

• mult
• nonn

Examples

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

Links

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

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).

Programs

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 *)