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.
Florian Breuer and Cameron Shaw-Carmody, Parity bias in fundamental units of real quadratic fields, Univ. Newcastle (Australia), Comp.-Assisted Res. Math. Appl. (2024). See pp. 1-4.
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
KEYWORD
nonn
AUTHOR
Warut Roonguthai, Aug 06 2007
STATUS
approved