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

Author

Warut Roonguthai, Aug 06 2007

Keywords

• nonn

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.