A059644 - OEIS

%I #11 Sep 08 2022 08:45:03

%S 3,5,11,13,19,29,37,43,53,59,61,67,83,101,107,109,131,139,149,157,163,

%T 173,179,181,197,211,227,229,233,251,269,277,283,293,307,317,331,347,

%U 349,373,379,389,397,419,421,443,461,467,491,499,509,523,541,547,557

%N Primes p such that x^58 = 2 has no solution mod p.

%C Complement of A049590 relative to A000040.

%H Vincenzo Librandi, <a href="/A059644/b059644.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^58 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[120]], ok] (* _Vincenzo Librandi_, Sep 21 2012 *)

%o (Magma) [p: p in PrimesUpTo(600) | not exists{x: x in ResidueClassRing(p) | x^58 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,2,58),print1(p,", ")));

%o /* _Joerg Arndt_, Sep 21 2012 */

%Y Cf. A000040, A049590.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Feb 02 2001