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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000040, A042966, A059667.

Programs

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

Mathematica

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