A216736 -id:A216736

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A051074

Primes p such that x^10 = -2 has a solution mod p.

+0
2

2, 3, 17, 19, 43, 59, 67, 73, 83, 89, 97, 107, 113, 137, 139, 163, 179, 193, 227, 233, 241, 251, 257, 283, 307, 313, 337, 347, 353, 379, 409, 419, 433, 443, 449, 457, 467, 499, 523, 547, 563, 569, 571, 577, 587, 593, 617, 619, 641, 643, 659, 673, 683, 739, 769, 787, 809, 827, 857, 859, 883, 907, 929, 937, 947, 953, 971, 977, 1009

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OFFSET

1,1

COMMENTS

Complement of A216736 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^10 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[500]], ok] (* Vincenzo Librandi, Sep 15 2012 *)

PROG

(PARI)

forprime(p=2, 2000, if([]~!=polrootsmod(x^10+2, p), print1(p, ", "))); print();

/* Joerg Arndt, Jun 24 2012 */

(Magma) [p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^10 eq - 2}]; // Vincenzo Librandi, Sep 15 2012

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Joerg Arndt, Jul 27 2011

STATUS

approved

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