A136679 a(n) is the number of ordered solutions (x,y,z) to x^2 + y^2 == z^2 mod n with 1 <= x,y,z <= n-1.

0, 0, 0, 9, 0, 16, 24, 45, 56, 48, 80, 137, 96, 144, 128, 315, 192, 302, 288, 425, 312, 400, 440, 621, 544, 528, 728, 969, 672, 704, 840, 1451, 880, 960, 984, 2021, 1152, 1296, 1248, 1901, 1440, 1504, 1680, 2569, 2024, 1936, 2024, 3387, 2400, 2524, 2240, 3561

Offset: 1

Author

Robert G. Wilson v, Apr 12 2008

Keywords

• nonn

Comments

Record values: 0, 9, 16, 24, 45, 56, 80, 137, 144, 315, 425, 440, 621, 728, 969, 1451, 2021, 2569, 3387, 3561, 4077, 4649, 6871, 8441, 9915, 10605, 11977, 14507, 16129, 20069, 20283, 22089, 28823, 41555, 41643, 43017, 51515, 56069, 65239, 65989, 72123, ....

Examples

			a(4)=9 because {1, 2, 1}, {1, 2, 3}, {2, 1, 1}, {2, 1, 3}, {2, 2, 2}, {2, 3, 1}, {2, 3, 3}, {3, 2, 1}, {3, 2, 3} are solutions for n=4.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..215..

Crossrefs

Cf. A137401.

Programs

Mathematica

f[n_] := Block[ {c = 0}, Do[ If[ Mod[x^2 + y^2, n] == Mod[z^2, n], c++ ], {x, n - 1}, {y, n - 1}, {z, n - 1}]; c]; Array[f, 52]