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Primes p == 5 (mod 8) such that the Diophantine equation x^2 - p*y^2 = -4 has a solution in odd integers x, y.
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%I #11 Oct 23 2023 14:39:04

%S 5,13,29,53,61,109,149,157,173,181,229,277,293,317,397,421,461,509,

%T 541,613,653,661,733,773,797,821,853,941,1013,1021,1061,1069,1093,

%U 1109,1117,1181,1229,1237,1277,1373,1381,1429,1453,1493,1549,1597

%N Primes p == 5 (mod 8) such that the Diophantine equation x^2 - p*y^2 = -4 has a solution in odd integers x, y.

%C 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)

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

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

%H Robin Visser, <a href="/A130230/b130230.txt">Table of n, a(n) for n = 1..10000</a>

%H Dario Alpern, <a href="https://www.alpertron.com.ar/QUAD.HTM">Generic two integer variable equation solver</a>.

%Y Cf. A130229.

%K nonn

%O 1,1

%A _Warut Roonguthai_, Aug 06 2007