A239434 Number of nonnegative integer solutions to the equation x^2 - 25*y^2 = n.

1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0

Offset

1,64

Comments

For (x, y) to be a solution to the more general equation x^2 - d^2*y^2 = n, it can be shown that n-f^2 must be divisible by 2*f*d, where f is a divisor of n not exceeding sqrt(n). Then y = (n-f^2)/(2*f*d) and x = d*y+f.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Example

a(64)=2 because x^2 - 25*y^2 = 64 has two solutions, (X,Y) = (8,0) and (17,3).

Prog

(PARI) a(n) = sumdiv(n, f, f^2<=n && (n-f^2)%(10*f)==0)

Crossrefs

Cf. A034178, A230240, A230263, A230264, A239435.

Sequence in context: A278929 A363738 A277143 * A033770 A216283 A262900

Adjacent sequences: A239431 A239432 A239433 * A239435 A239436 A239437

Keyword

nonn

Author

Colin Barker, Mar 18 2014

Status

approved