A216747 -id:A216747 - cp's OEIS frontend

A051085 Primes p such that x^32 = -2 has a solution mod p.

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

Offset: 1

N. J. A. Sloane

Complement of A216747 relative to A000040. - Vincenzo Librandi, Sep 17 2012

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

Cf. A163183.

[p: p in PrimesUpTo(1200) | exists(t){x : x in ResidueClassRing(p) | x^32 eq - 2}]; // Vincenzo Librandi, Sep 15 2012

ok[p_]:= Reduce[Mod[x^32 + 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[400]], ok] (* Vincenzo Librandi, Sep 15 2012 *)

forprime(p=2, 2000, if([]~!=polrootsmod(x^32+2, p), print1(p, ", "))); print();
/* Joerg Arndt, Jun 24 2012 */

More terms from Joerg Arndt, Jul 27 2011

A059349 Primes p such that x^32 = 2 has no solution mod p.

Original entry on oeis.org

3, 5, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 83, 97, 101, 107, 109, 113, 131, 137, 139, 149, 157, 163, 173, 179, 181, 193, 197, 211, 227, 229, 241, 251, 257, 269, 277, 281, 283, 293, 307, 313, 317, 331, 347, 349, 353, 373, 379, 389, 397, 401, 409, 419

Offset: 1

Klaus Brockhaus, Jan 27 2001

Complement of A049564 relative to A000040.
Differs from A014662 first at p=6529, then at p=21569. [R. J. Mathar, Oct 05 2008]
Differs from A045316 (x^8 == 2 (mod p) has no solution) first at a(37) = 257 which is not a term of A045316. See A070184 for all such terms. - M. F. Hasler, Jun 21 2024

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

Cf. A000040, A049564, A216747.

Cf. A070184 = (this sequence) \ A045316.

[p: p in PrimesUpTo(450) | not exists{x : x in ResidueClassRing(p) | x^32 eq 2 }]; // Vincenzo Librandi, Sep 20 2012

ok[p_] := Reduce[Mod[x^32 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok ] (* Vincenzo Librandi, Sep 20 2012  *)

cp's OEIS Frontend

A051085 Primes p such that x^32 = -2 has a solution mod p.

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