A238240 Positive integers n such that x^2 - 20xy + y^2 + n = 0 has integer solutions.

18, 35, 50, 63, 72, 74, 83, 90, 95, 98, 99, 107, 140, 162, 171, 200, 215, 227, 252, 266, 275, 288, 296, 315, 332, 347, 359, 360, 362, 371, 380, 387, 392, 395, 396, 407, 428, 450, 491, 495, 530, 539, 560, 567, 602, 623, 626, 635, 648, 666, 684, 695, 711, 722, 743, 747, 755, 770, 791, 794, 800, 810

Offset: 1

Author

Colin Barker, Feb 20 2014

Keywords

• nonn

Comments

Positive integers n such that x^2 - 99 y^2 + n = 0 has integer solutions. - Robert Israel, Oct 22 2024

Examples

			63 is in the sequence because x^2 - 20xy + y^2 + 63 = 0 has integer solutions, for example (x, y) = (1, 16).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A075839 (n = 18), A221763 (n = 63), A198947 (n = 90), A001085 (n = 99).

Cf. A031363, A084917, A237351, A237599, A237606, A237609, A237610, A236330, A236331.

Programs

Maple

filter:= t -> [isolve(99*y^2 - z^2 = t)] <> []:
select(filter, [$1..1000]); # Robert Israel, Oct 22 2024

Extensions

Corrected by Robert Israel, Oct 22 2024