A130229 Primes p == 5 (mod 8) such that the Diophantine equation x^2 - p*y^2 = -4 has no solution in odd integers x, y.

37, 101, 197, 269, 349, 373, 389, 557, 677, 701, 709, 757, 829, 877, 997, 1213, 1301, 1613, 1861, 1901, 1949, 1973, 2069, 2221, 2269, 2341, 2357, 2621, 2797, 2837, 2917, 3109, 3181, 3301, 3413, 3709, 3797, 3821, 3853, 3877, 4013, 4021, 4093

Offset

1,1

Comments

For the Diophantine equation x^2 - p*y^2 = -4 to have a solution in odd integers x, y we must have p == 5 (mod 8).

Calculated using Dario Alpern's quadratic Diophantine solver, see link.

Suggested by a discussion on the Number Theory Mailing List, circa Aug 01 2007.

Links

Robin Visser, Table of n, a(n) for n = 1..10000

Dario Alpern, Generic two integer variable equation solver.

Florian Breuer, Periods of Ducci sequences and odd solutions to a Pellian equation, University of Newcastle, Australia, 2018.

J. Xue, T.-C. Yang, C.-F. Yu, Supersingular abelian surfaces and Eichler class number formula, arXiv preprint arXiv:1404.2978, 2014

Jiangwei Xue, TC Yang, CF Yu, Numerical Invariants of Totally Imaginary Quadratic Z[sqrt{p}]-orders, arXiv preprint arXiv:1603.02789, 2016

Crossrefs

Cf. A130230.

Sequence in context: A108160 A044224 A044605 * A142941 A176973 A105019

Adjacent sequences: A130226 A130227 A130228 * A130230 A130231 A130232

Keyword

nonn

Author

Warut Roonguthai, Aug 06 2007

Status

approved