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A051101
Primes p such that x^64 = -2 has a solution mod p.
5
2, 3, 11, 19, 43, 59, 67, 83, 107, 131, 139, 163, 179, 211, 227, 251, 281, 283, 307, 331, 347, 379, 419, 443, 467, 491, 499, 523, 547, 563, 571, 587, 617, 619, 643, 659, 683, 691, 739, 787, 811, 827, 859, 883, 907, 947, 971, 1019, 1033, 1049, 1051, 1091, 1097, 1123, 1163, 1171, 1187
OFFSET
1,1
COMMENTS
Differs from A051085 first at the 541st entry, at p=15809. - R. J. Mathar, Oct 14 2008
From Christopher J. Smyth, Jul 24 2009: (Start)
Differs from A163183 (primes dividing 2^j+1 for some odd j) at the 827th entry, at p=25601. See comment at A163186 for explanation.
Sequence is union of A163183 and A163186 (primes p such that the equation x^64 = -2 mod p has a solution, and ord_p(-2) is even).
(End)
Complement of A216777 relative to A000040. - Vincenzo Librandi, Sep 17 2012
MATHEMATICA
ok[p_]:= Reduce[Mod[x^64 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[400]], ok] (* Vincenzo Librandi, Sep 16 2012 *)
PROG
(PARI)
forprime(p=2, 2000, if([]~!=polrootsmod(x^64+2, p), print1(p, ", "))); print();
/* Joerg Arndt, Jun 24 2012 */
(Magma) [p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^64 eq - 2}]; // Vincenzo Librandi, Sep 16 2012
CROSSREFS
Sequence in context: A051073 A051077 A051085 * A045339 A051091 A085902
KEYWORD
nonn,easy
EXTENSIONS
More terms from Joerg Arndt, Jul 27 2011
STATUS
approved