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Primes p such that x^12 = 2 has no solution mod p.
7

%I #15 Nov 08 2016 22:28:50

%S 3,5,7,11,13,17,19,29,37,41,43,53,59,61,67,73,79,83,97,101,103,107,

%T 109,131,137,139,149,151,157,163,173,179,181,193,197,199,211,227,229,

%U 241,251,269,271,277,283,293,307,313,317,331,337,347,349,367,373,379,389

%N Primes p such that x^12 = 2 has no solution mod p.

%C Complement of A049544 relative to A000040.

%C Coincides for the first 119 terms with sequence of primes p such that x^36 = 2 has no solution mod p (first divergence is at 919, cf. A059668).

%H Vincenzo Librandi, <a href="/A059264/b059264.txt">Table of n, a(n) for n = 1..5000</a>

%t ok[p_] := Reduce[Mod[x^12 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]],ok] (* _Vincenzo Librandi_, Sep 14 2012 *)

%t Select[ Prime@ Range@ PrimePi@400, !MemberQ[ PowerMod[ Range@#, 12, #], Mod[2, #]] &] (* _Robert G. Wilson v_, Nov 05 2016 after _Bruno Berselli_ in A059362 *)

%Y Cf. A000040, A049544, A049568, A059668.

%K easy,nonn

%O 1,1

%A _Klaus Brockhaus_, Jan 23 2001