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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
KEYWORD
mult,nonn
AUTHOR
T. D. Noe, Jun 15 2004
STATUS
approved

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)