A091968 Primes congruent to 3 (mod 16).

3, 19, 67, 83, 131, 163, 179, 211, 227, 307, 419, 467, 499, 547, 563, 643, 659, 691, 739, 787, 883, 947, 1091, 1123, 1171, 1187, 1283, 1427, 1459, 1523, 1571, 1619, 1667, 1699, 1747, 1811, 1907, 1987, 2003, 2083, 2099, 2131, 2179, 2243, 2339, 2371, 2467

Offset: 1

Author

Giovanni Teofilatto, Mar 14 2004

Keywords

• nonn
• easy

Comments

For any n, the equations x^4 - y^4 = a(n)*z^2 and x^4 - a(n)^2*y^4 = z^2 are not solvable in natural numbers. - Arkadiusz Wesolowski, Aug 15 2013

References

• L. J. Mordell, Diophantine Equations, Ac. Press, p. 23.
• Trygve Nagell, Introduction to Number Theory, Chelsea Publishing Company, NY, 1964, p. 230.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A092022, A093012.

Programs

Mathematica

Select[Prime@Range[400], Mod[ #, 16] == 3 &] (* Ray Chandler, Dec 06 2006 *)

PARI

is(n)=isprime(n) && n%16==3 \\ Charles R Greathouse IV, Jul 01 2016

Extensions

More terms from Ray Chandler, Mar 15 2004