A051071 Primes p such that x^4 = -2 has a solution mod p.

2, 3, 11, 19, 43, 59, 67, 73, 83, 89, 107, 113, 131, 139, 163, 179, 211, 227, 233, 251, 257, 281, 283, 307, 331, 337, 347, 353, 379, 419, 443, 467, 491, 499, 523, 547, 563, 571, 577, 587, 593, 601, 617, 619, 643, 659, 683, 691, 739, 787, 811, 827, 859, 881, 883, 907, 937, 947, 971, 1019, 1033, 1049, 1051, 1091, 1097, 1123

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A216690 relative to A000040. - Vincenzo Librandi, Sep 16 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

[p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^4 eq - 2}]; // Vincenzo Librandi, Sep 15 2012

Mathematica

ok[p_]:= Reduce[Mod[x^4 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 15 2012 *)

PARI

forprime(p=2,2000,if([]~!=polrootsff(x^4+2,p,y-1),print1(p,", ")));print();
/* or: */
forprime(p=2,2000,if([]~!=polrootsmod(x^4+2,p),print1(p,", ")));print();
/* faster */ /* Joerg Arndt, Jul 27 2011 */

Extensions

More terms from Joerg Arndt, Jul 27 2011