A049569 Primes p such that x^37 = 2 has a solution mod p.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Complement of A059223 relative to A000040. - Vincenzo Librandi, Sep 14 2012

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000
• Index entries for related sequences

Crossrefs

Cf. A000040, A059223.

Programs

Magma

[p: p in PrimesUpTo(300) | exists(t){x : x in ResidueClassRing(p) | x^37 eq 2}]; // Vincenzo Librandi, Sep 14 2012

Mathematica

ok[p_]:= Reduce[Mod[x^37 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

PARI

N=10^4;  default(primelimit,N);
ok(p, r, k)={ return ( (p==r) || (Mod(r,p)^((p-1)/gcd(k,p-1))==1) ); }
forprime(p=2,N, if (ok(p,2,37),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */