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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 23 13:17 EDT 2019. Contains 321430 sequences. (Running on oeis4.)