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Primes p such that x^3 = 15 has no solution mod p.
3

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

%S 13,19,37,43,61,73,97,103,109,127,139,151,157,163,181,193,199,211,241,

%T 271,307,313,337,349,373,379,409,421,433,439,457,487,499,523,547,577,

%U 601,607,613,619,631,661,691,709

%N Primes p such that x^3 = 15 has no solution mod p.

%C Complement of A040069 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012

%H Vincenzo Librandi, <a href="/A040070/b040070.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^3 - 15, 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 15} ]; // _Vincenzo Librandi_, Sep 17 2012

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.