

A042966


Primes p such that x^7 = 2 has a solution mod p.


11



2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 37, 41, 47, 53, 59, 61, 67, 73, 79, 83, 89, 97, 101, 103, 107, 109, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 199, 223, 227, 229, 233, 241, 251, 257, 263, 269, 271, 277, 283, 293, 307, 311, 313, 317, 331
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OFFSET

1,1


COMMENTS

Coincides with sequence of "primes p such that x^49 = 2 has a solution mod p" for first 572 terms, then diverges.
a(98) = 631 is the first such prime that is congruent to 1 (mod 7).  Georg Fischer, Jan 06 2022


LINKS



MATHEMATICA

ok[p_]:= Reduce[Mod[x^7  2, p] == 0, x, Integers]=!=False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 13 2012 *)


PROG

(Magma) [p: p in PrimesUpTo(400)  exists{x: x in ResidueClassRing(p)  x^7 eq 2}]; // Bruno Berselli, Sep 12 2012


CROSSREFS

For primes p such that x^m == 2 mod p has a solution for m = 2,3,4,5,6,7,... see A038873, A040028, A040098, A040159, A040992, A042966, ...


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



