%I #15 Sep 08 2022 08:45:03
%S 3,5,11,13,17,19,23,29,37,41,43,53,59,61,67,83,89,97,101,107,109,131,
%T 137,139,149,157,163,173,179,181,193,197,199,211,227,229,241,251,269,
%U 277,283,293,307,313,317,331,347,349,353,373,379,389,397,401,409,419
%N Primes p such that x^44 = 2 has no solution mod p.
%C Complement of A049576 relative to A000040.
%H Vincenzo Librandi, <a href="/A059636/b059636.txt">Table of n, a(n) for n = 1..1000</a>
%t ok[p_] := Reduce[Mod[x^44 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[90]], ok] (* _Vincenzo Librandi_, Sep 21 2012 *)
%o (Magma) [p: p in PrimesUpTo(500) | not exists{x: x in ResidueClassRing(p) | x^44 eq 2}]; // _Vincenzo Librandi_, Sep 21 2012
%o (PARI)
%o N=10^4; default(primelimit,N);
%o ok(p, r, k)={ return ( (p==r) || (Mod(r,p)^((p-1)/gcd(k,p-1))==1) ); }
%o forprime(p=2,N, if (! ok(p,2,44),print1(p,", ")));
%o /* _Joerg Arndt_, Sep 21 2012 */
%Y Cf. A000040, A049576.
%K nonn,easy
%O 1,1
%A _Klaus Brockhaus_, Feb 02 2001