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A042967 Primes p such that x^7 = 2 has no solution mod p. 4
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 (list; graph; refs; listen; history; text; internal format)
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.

Sequence in context: A004619 A140444 A042969 * A061638 A136062 A039348

Adjacent sequences:  A042964 A042965 A042966 * A042968 A042969 A042970

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 18 02:57 EST 2020. Contains 332006 sequences. (Running on oeis4.)