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Primes p such that x^3 = 12 has no solution mod p.
2

%I #12 Sep 08 2022 08:44:53

%S 7,31,37,43,61,67,73,103,109,127,139,151,157,163,181,193,223,229,241,

%T 271,277,283,313,337,349,367,379,397,409,421,433,457,523,541,547,571,

%U 577,601,607,613,619,631,661,691

%N Primes p such that x^3 = 12 has no solution mod p.

%C Complement of A040062 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012

%H Vincenzo Librandi, <a href="/A040064/b040064.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^3 - 12, p] == 0, x, Integers] == False;Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 17 2012 *)

%o (Magma) [p: p in PrimesUpTo(1000) | not exists{x : x in ResidueClassRing(p) | x^3 eq 12} ]; // _Vincenzo Librandi_, Sep 17 2012

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.