

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.


1



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
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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 at http://www.alpertron.com.ar/QUAD.HTM
Suggested by a discussion on the Number Theory Mailing List, circa Aug 01 2007.


LINKS

Table of n, a(n) for n=1..43.
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



