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A059641 Primes p such that x^52 = 2 has no solution mod p. 2

%I

%S 3,5,11,13,17,19,29,37,41,43,53,59,61,67,79,83,97,101,107,109,131,137,

%T 139,149,157,163,173,179,181,193,197,211,227,229,241,251,269,277,283,

%U 293,307,313,317,331,347,349,373,379,389,397,401,409,419,421,433,443

%N Primes p such that x^52 = 2 has no solution mod p.

%C Complement of A049584 relative to A000040.

%H Vincenzo Librandi, <a href="/A059641/b059641.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^52 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok] (* _Vincenzo Librandi_, Sep 21 2012 *)

%o (MAGMA) [p: p in PrimesUpTo(500) | not exists{x: x in ResidueClassRing(p) | x^52 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,2,52),print1(p,", ")));

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

%Y Cf. A000040, A049584.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Feb 02 2001

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Last modified June 22 10:52 EDT 2021. Contains 345375 sequences. (Running on oeis4.)