login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..2500

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

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

Cf. A208895, A086932, A089003, A060968, A087784.

Sequence in context: A278374 A300658 A089330 * A108270 A019161 A291718

Adjacent sequences:  A227550 A227551 A227552 * A227554 A227555 A227556

KEYWORD

nonn,mult

AUTHOR

José María Grau Ribas, Jul 16 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 20 20:12 EDT 2019. Contains 327247 sequences. (Running on oeis4.)