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

1,1

Comments

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

Links

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A213894 A294668 A095282 * A051095 A051073 A051077

Adjacent sequences: A051068 A051069 A051070 * A051072 A051073 A051074

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Joerg Arndt, Jul 27 2011

Status

approved