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Primes p such that x^5 = 7 has no solution mod p.
2

%I #13 Jun 19 2023 04:21:51

%S 11,31,41,61,71,101,131,151,191,211,241,251,271,281,331,401,421,431,

%T 461,491,521,541,571,601,631,641,691,701,751,761,821,881,941,991,1021,

%U 1051,1061,1091,1181,1231,1291

%N Primes p such that x^5 = 7 has no solution mod p.

%C Complement of A040171 relative to A000040. - _Vincenzo Librandi_, Sep 18 2012

%H Vincenzo Librandi, <a href="/A040172/b040172.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^5 - 7, p] == 0, x, Integers] == False; Select[Prime[Range[300]], ok] (* _Vincenzo Librandi_, Sep 18 2012 *)

%o (Magma) [p: p in PrimesUpTo(1500) | not exists{x : x in ResidueClassRing(p) | x^5 eq 7} ]; // _Vincenzo Librandi_, Sep 18 2012

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_