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Primes p such that x^3 = 10 has a solution mod p.
2

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

%S 2,3,5,11,17,23,29,37,41,47,53,59,71,73,79,83,89,101,103,107,113,127,

%T 131,137,139,149,167,173,179,191,197,227,233,239,251,257,263,269,271,

%U 281,293,311,317,331,347,349,353

%N Primes p such that x^3 = 10 has a solution mod p.

%C Complement of A040058 relative to A000040. - _Vincenzo Librandi_, Sep 13 2012

%H Vincenzo Librandi, <a href="/A040054/b040054.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[180]], ok] (* _Vincenzo Librandi_, Sep 11 2012 *)

%o (Magma) [p: p in PrimesUpTo(450) | exists(t){x : x in ResidueClassRing(p) | x^3 eq 10}]; // _Vincenzo Librandi_, Sep 11 2012

%Y Cf. A000040, A040058.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.