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 A049569 Primes p such that x^37 = 2 has a solution mod p. 2

%I

%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,

%T 97,101,103,107,109,113,127,131,137,139,151,157,163,167,173,179,181,

%U 191,193,197,199,211,227,229,233,239,241,251,257,263,269,271,277,281

%N Primes p such that x^37 = 2 has a solution mod p.

%C Complement of A059223 relative to A000040. - _Vincenzo Librandi_, Sep 14 2012

%H R. J. Mathar, <a href="/A049569/b049569.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Pri#smp">Index entries for related sequences</a>

%t ok[p_]:= Reduce[Mod[x^37 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* _Vincenzo Librandi_, Sep 14 2012 *)

%o (MAGMA) [p: p in PrimesUpTo(300) | exists(t){x : x in ResidueClassRing(p) | x^37 eq 2}]; // _Vincenzo Librandi_, Sep 14 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,2,37),print1(p,", ")));

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

%Y Cf. A000040, A059223.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

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Last modified September 30 05:03 EDT 2020. Contains 337435 sequences. (Running on oeis4.)