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A051097
Primes p such that x^56 = -2 has a solution mod p.
2
2, 3, 11, 19, 59, 67, 83, 107, 131, 139, 163, 179, 227, 251, 257, 283, 307, 331, 347, 419, 443, 467, 499, 523, 563, 571, 587, 619, 643, 683, 691, 739, 787, 811, 859, 881, 907, 947, 971, 1019, 1033, 1049, 1091, 1097, 1123, 1163, 1171, 1187, 1193, 1217, 1249, 1259, 1283, 1291, 1307, 1427, 1451, 1459, 1481, 1483, 1523, 1531, 1553, 1571, 1579
OFFSET
1,1
COMMENTS
Complement of A216773 relative to A000040. - Vincenzo Librandi, Sep 17 2012
LINKS
MATHEMATICA
ok[p_]:= Reduce[Mod[x^56 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[500]], ok] (* Vincenzo Librandi, Sep 16 2012 *)
PROG
(PARI) forprime(p=2, 2000, if([]~!=polrootsff(x^56+2, p, y-1), print1(p, ", "))); print();
/* or: */
forprime(p=2, 2000, if([]~!=polrootsmod(x^56+2, p), print1(p, ", "))); print(); /* faster */
/* Joerg Arndt, Jul 27 2011 */
(Magma) [p: p in PrimesUpTo(1600) | exists(t){x : x in ResidueClassRing(p) | x^56 eq - 2}]; // Vincenzo Librandi, Sep 16 2012
CROSSREFS
Sequence in context: A051091 A085902 A051083 * A214773 A235618 A076201
KEYWORD
nonn,easy
EXTENSIONS
More terms from Joerg Arndt, Jul 27 2011
STATUS
approved