A264348 Exceptional odd numbers D that do not admit a solution to the Pell equation x^2 - D y^2 = +8 with both x and y odd.

257, 401, 577, 697, 761, 1009, 1129, 1297, 1393, 1489, 1601, 1897, 2081, 2153, 2177, 2329, 2713, 2777, 2857, 2993, 3121, 3137, 3281, 3889, 4001

Offset: 1

Author

Wolfdieter Lang, Nov 17 2015

Keywords

• nonn

Comments

These are the odd numbers 1 (mod 8), not a square, having in the composite case no prime factors 3 or 5 (mod 8), and the indefinite binary quadratic form x^2 - D*y^2 (with discriminant 4*D > 0) does not represent +8.

The odd numbers D which admit proper solutions to the Pell equation x^2 - D*y^2 = +8 with both x and y odd are given by A263012.

Crossrefs

Cf. A263011, A263012.