A130230 Primes p == 5 (mod 8) such that the Diophantine equation x^2 - p*y^2 = -4 has a solution in odd integers x, y.

5, 13, 29, 53, 61, 109, 149, 157, 173, 181, 229, 277, 293, 317, 397, 421, 461, 509, 541, 613, 653, 661, 733, 773, 797, 821, 853, 941, 1013, 1021, 1061, 1069, 1093, 1109, 1117, 1181, 1229, 1237, 1277, 1373, 1381, 1429, 1453, 1493, 1549, 1597

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.

Crossrefs

Cf. A130229.

Sequence in context: A194270 A194700 A220500 * A106931 A078370 A308464

Adjacent sequences: A130227 A130228 A130229 * A130231 A130232 A130233

Keyword

nonn

Author

Warut Roonguthai, Aug 06 2007

Status

approved