A042967 - OEIS

A042967

Primes p such that x^7 = 2 has no solution mod p.

29, 43, 71, 113, 127, 197, 211, 239, 281, 337, 379, 421, 449, 463, 491, 547, 617, 659, 701, 743, 757, 827, 883, 911, 967, 1009, 1051, 1093, 1289, 1303, 1373, 1429, 1471, 1499, 1583, 1597, 1667, 1723, 1877, 1933, 2017, 2087, 2129, 2213, 2269, 2297, 2311, 2339, 2381, 2423, 2437, 2521

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OFFSET

1,1

COMMENTS

Complement of A042966 relative to A000040. Coincides for the first 96 terms with the sequence of primes p such that x^49 = 2 has no solution mod p (first divergence is at 4999, cf. A059667). - Klaus Brockhaus, Feb 04 2001

LINKS

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

EXAMPLE

x^7 = 2 has no solution mod 29, so 29 is in the sequence.

8^7 = 2097152 and (2097152 - 2)/31 = 67650, so 31 is not in the sequence.

MATHEMATICA

sevPow2ModPQ[p_] := Reduce[Mod[x^7 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[700]], sevPow2ModPQ] (* Vincenzo Librandi, Sep 19 2012 *)

PROG

(Magma) [p: p in PrimesUpTo(3000) | forall{x: x in ResidueClassRing(p) | x^7 ne 2}]; // Vincenzo Librandi, Aug 21 2012

(Magma) [p: p in PrimesUpTo(2600) | not exists{x : x in ResidueClassRing(p) | x^7 eq 2} ]; // Vincenzo Librandi, Sep 19 2012

CROSSREFS

Cf. A000040, A042966, A059667.