A137351 Composite numbers n such that x^2 - n*y^2 represents -1.

10, 26, 50, 58, 65, 74, 82, 85, 106, 122, 125, 130, 145, 170, 185, 202, 218, 226, 250, 265, 274, 290, 298, 314, 325, 338, 346, 362, 365, 370, 394, 425, 442, 445, 458, 481, 485, 493, 530, 533, 538, 554, 565, 586, 610, 626, 629, 634, 685, 697, 698, 730, 746

Offset: 1

Author

N. J. A. Sloane, Apr 08 2008

Keywords

• nonn

Comments

Number of terms less than or equal to 10^k for k=0 .. : 0, 1, 8, 71, 712, 6702, 63485, 602870, ... . - Robert G. Wilson v, Jul 20 2008

Examples

			3^2 - 10*1^2 = -1, so 10 is a member.
4005^2 - 106*389^2 = -1, so 106 is a member.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..63485
• J. P. Robertson and K. R. Matthews, A continued fraction approach to a result of Feit, Amer. Math. Monthly, 115 (No. 4, 2008), 346-349.
• Eric Weisstein's World of Mathematics, Pell Equation.

Crossrefs

For the primes with this property see A002313. A134406 is a subset.

Programs

Mathematica

lst = {}; Do[ If[ !PrimeQ@ n && FindInstance[x^2 - n*y^2 == -1, {x, y}, Integers] != {}, AppendTo[lst, n]], {n, 2, 1000}]

Extensions

More terms from Robert G. Wilson v, Jul 20 2008