%I #11 Sep 08 2022 08:44:53

%S 2,17,19,43,47,59,67,83,103,127,149,151,157,179,191,223,229,239,251,

%T 257,263,271,293,307,331,353,359,383,389,409,433,443,457,463,467,491,

%U 509,523,563,587,599,613,631,647

%N Primes p such that x^4 = 17 has a solution mod p.

%H Vincenzo Librandi, <a href="/A040138/b040138.txt">Table of n, a(n) for n = 1..1000</a>

%t ok [p_]:=Reduce[Mod[x^4 - 17, p]== 0, x, Integers]=!= False; Select[Prime[Range[180]], ok] (* _Vincenzo Librandi_, Sep 12 2012 *)

%o (Magma) [p: p in PrimesUpTo(800) | exists{x: x in ResidueClassRing(p) | x^4 eq 17}]; // _Vincenzo Librandi_, Sep 12 2012

%o (PARI) /* with workaround for bug with ispower( Mod(17,n), 4) "division by zero" */

%o select( n->(n==2) || (ispower( Mod(17,n), 4)), primes(1000) )

%o /* _Joerg Arndt_, Sep 12 2012 */

%Y Cf. A040140.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.