A040058 - OEIS

%I #14 Sep 08 2022 08:44:53

%S 7,13,19,31,43,61,67,97,109,151,157,163,181,193,199,211,223,229,241,

%T 277,283,307,313,337,367,373,379,397,409,433,439,487,499,523,541,571,

%U 577,601,619,631,709,727,757,769

%N Primes p such that x^3 = 10 has no solution mod p.

%C Complement of A040054 relative to A000040. - _Vincenzo Librandi_, Sep 17 2012

%H Vincenzo Librandi, <a href="/A040058/b040058.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^3 - 10, 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 10} ]; // _Vincenzo Librandi_, Sep 17 2012

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.