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Primes p such that x^15 = 2 has no solution mod p.
2

%I #10 Sep 08 2022 08:45:02

%S 7,11,13,19,31,37,41,61,67,71,73,79,97,101,103,131,139,151,163,181,

%T 191,193,199,211,241,271,281,311,313,331,337,349,367,373,379,401,409,

%U 421,461,463,487,491,521,523,541,547,571,577,601,607,613,619,631,661,673

%N Primes p such that x^15 = 2 has no solution mod p.

%C Complement of A049547 relative to A000040.

%H Vincenzo Librandi, <a href="/A059308/b059308.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^15 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[150]], ok] (* _Vincenzo Librandi_, Sep 20 2012 *)

%o (Magma) [p: p in PrimesUpTo(700) | not exists{x: x in ResidueClassRing(p) | x^15 eq 2}]; // _Vincenzo Librandi_, Sep 20 2012

%Y Cf. A000040, A049547.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Jan 25 2001