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A059637 Primes p such that x^45 = 2 has no solution mod p. 2

%I

%S 7,11,13,19,31,37,41,61,67,71,73,79,97,101,103,109,131,139,151,163,

%T 181,191,193,199,211,241,271,281,307,311,313,331,337,349,367,373,379,

%U 401,409,421,433,461,463,487,491,521,523,541,547,571,577,601,607,613,619

%N Primes p such that x^45 = 2 has no solution mod p.

%C Complement of A049577 relative to A000040.

%H Vincenzo Librandi, <a href="/A059637/b059637.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^45 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[120]], ok] (* _Vincenzo Librandi_, Sep 21 2012 *)

%o (MAGMA) [p: p in PrimesUpTo(700) | not exists{x: x in ResidueClassRing(p) | x^45 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,2,45),print1(p,", ")));

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

%Y Cf. A000040, A049577.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Feb 02 2001

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Last modified September 17 05:34 EDT 2021. Contains 347478 sequences. (Running on oeis4.)