A237351 Positive integers k such that x^2 - 5xy + y^2 + k = 0 has integer solutions.

3, 5, 12, 17, 20, 21, 27, 35, 41, 45, 47, 48, 59, 68, 75, 80, 83, 84, 89, 101, 108, 111, 119, 125, 129, 131, 140, 147, 153, 164, 167, 173, 180, 185, 188, 189, 192, 201, 215, 227, 236, 237, 243, 245, 251, 255, 257, 269, 272, 287, 293, 300, 311, 315, 320, 327

Offset: 1

Author

Colin Barker, Feb 06 2014

Keywords

• nonn

Comments

See comments on method used in A084917.

The equivalent sequence for x^2 - 3xy + y^2 + k = 0 is A031363.

The equivalent sequence for x^2 - 4xy + y^2 + k = 0 is A084917.

Positive numbers of the form 3x^2 - 7y^2. - Jon E. Schoenfield, Jun 03 2022

Examples

			12 is in the sequence because x^2 - 5xy + y^2 + 12 = 0 has integer solutions, for example, (x, y) = (2, 8).
		

Links

• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A004253 (k = 3), A237254 (k = 5), A237255 (k = 17).

Cf. A031363, A084917.

For primes see A141160.

Programs

Mathematica

Select[Range[350],Length[FindInstance[x^2-5x y+y^2+#==0,{x,y},Integers]]>0&] (* Harvey P. Dale, Apr 23 2023 *)