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A059257 Primes p such that x^47 = 2 has no solution mod p. 2

%I #22 Sep 08 2022 08:45:02

%S 283,659,941,1129,1223,1693,1787,2069,2351,2539,2633,3761,4231,4513,

%T 4889,5077,5171,5641,5923,6299,6581,6863,7333,8179,8273,8461,8837,

%U 9871,10247,10529,11093,11657,11939,12409,12503,12973,13537,13913,14759

%N Primes p such that x^47 = 2 has no solution mod p.

%C Presumably this is also Primes congruent to 1 mod 47. - _N. J. A. Sloane_, Jul 11 2008. Not so! The smallest counterexample is 26227: 26227 == 1 (mod 47), but 131^47 == 2 (mod 26227), therefore this prime is not in the sequence. - _Bruno Berselli_, Sep 12 2012

%C All terms are 1 mod 94. - _Charles R Greathouse IV_, Sep 13 2012

%C Complement of A216885 relative to A000040. - _Vincenzo Librandi_, Sep 20 2012

%H Vincenzo Librandi, <a href="/A059257/b059257.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^47 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[1800]], ok] (* _Vincenzo Librandi_, Sep 20 2012 *)

%o (Magma) [p: p in PrimesUpTo(15000) | forall{x: x in ResidueClassRing(p) | x^47 ne 2}]; // _Bruno Berselli_, Sep 12 2012

%o (PARI) select(p->!ispower(Mod(2,p),47),primes(3000)) \\ _Charles R Greathouse IV_, Sep 13 2012

%Y Cf. A000040, A058853.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Jan 23 2001

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)