A237610 Positive integers k such that x^2 - 10xy + y^2 + k = 0 has integer solutions.

8, 15, 20, 23, 24, 32, 47, 60, 71, 72, 80, 87, 92, 95, 96, 116, 128, 135, 152, 159, 167, 180, 188, 191, 200, 207, 212, 215, 216, 239, 240, 263, 276, 284, 288, 303, 311, 320, 335, 344, 348, 359, 368, 375, 380, 383, 384, 392, 404, 423, 431, 447, 456, 464, 479

Offset: 1

Author

Colin Barker, Feb 10 2014

Keywords

• nonn

Examples

			15 is in the sequence because x^2 - 10xy + y^2 + 15 = 0 has integer solutions, for example (x, y) = (2, 19).
		

Crossrefs

Cf. A072256 (k = 8), A129445 (k = 15), A080806 (k = 20), A074061 (k = 23), A001079 (k = 24).

Cf. A031363, A084917, A237351, A237599, A237606, A237609.

Programs

PARI

is(n)=m=bnfisintnorm(bnfinit(x^2-10*x+1),-n);#m>0&&denominator(polcoeff(m[1],1))==1 \\ Ralf Stephan, Feb 11 2014