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A227553
Number of solutions to x^2 - y^2 - z^2 == 1 (mod n).
2
1, 4, 6, 8, 30, 24, 42, 32, 54, 120, 110, 48, 182, 168, 180, 128, 306, 216, 342, 240, 252, 440, 506, 192, 750, 728, 486, 336, 870, 720, 930, 512, 660, 1224, 1260, 432, 1406, 1368, 1092, 960, 1722, 1008, 1806, 880, 1620, 2024, 2162, 768, 2058, 3000, 1836
OFFSET
1,2
COMMENTS
Conjecture: a(2) = 4; if s > 1 then a(2^s) = 2^(2s-1); if p == 1 (mod 4) then a(p^s) = (p+1)*p^(2s-1); if p == 3 (mod 4) then a(p^s) = (p-1)*p^(2s-1).
MATHEMATICA
a[1] = 1; a[n_] := Sum[If[Mod[a^2-b^2-c^2, n] == 1, 1, 0], {a, n}, {b, n}, {c, n}]; Table[a[n], {n, 10}]
PROG
(PARI)
M(n, f)={sum(i=0, n-1, Mod(x^(f(i)%n), x^n-1))}
a(n)={polcoeff(lift(M(n, i->i^2) * M(n, i->-(i^2))^2 ), 1%n)} \\ Andrew Howroyd, Jun 24 2018
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
STATUS
approved