A212376 Primes p such that x^48 = 2 has no solution mod p.

3, 5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 73, 79, 83, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 193, 197, 199, 211, 227, 229, 241, 251, 269, 271, 277, 281, 283, 293, 307, 313, 317, 331, 337, 347, 349, 353, 367

Offset: 1

Author

Bruno Berselli, Sep 14 2012

Keywords

• nonn
• easy

Comments

Complement of A049580 relative to A000040.

This sequence is not the same as A059362. First disagreement at index 162: a(162)=1217, A059362(162)=1229.

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A049580.

Cf. A059362.

Programs

Magma

[p: p in PrimesUpTo(400) | forall{x: x in ResidueClassRing(p) | x^48 ne 2}];

Mathematica

Select[Prime[Range[PrimePi[400]]], ! MemberQ[PowerMod[Range[#], 48, #], Mod[2, #]] &]
ok[p_] := Reduce[Mod[x^48 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[75]], ok] (* Vincenzo Librandi, Sep 21 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,2,48),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */