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Primes p such that x^4 = 21 has a solution mod p.
2

%I #9 Sep 08 2022 08:44:53

%S 2,3,5,7,17,43,47,59,67,79,83,109,127,131,151,163,167,193,211,227,251,

%T 269,311,331,337,353,373,379,383,419,463,467,479,487,499,503,509,521,

%U 547,563,571,587,593,631,647,709

%N Primes p such that x^4 = 21 has a solution mod p.

%H Vincenzo Librandi, <a href="/A040149/b040149.txt">Table of n, a(n) for n = 1..1000</a>

%t ok [p_]:=Reduce[Mod[x^4 - 21, p]== 0, x, Integers]=!= False; Select[Prime[Range[180]], ok] (* _Vincenzo Librandi_, Sep 12 2012 *)

%o (Magma) [p: p in PrimesUpTo(800) | exists(t){x : x in ResidueClassRing(p) | x^4 eq 21}]; // _Vincenzo Librandi_, Sep 12 2012

%Y Cf. A040150.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.