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A059258 Primes p such that x^53 = 2 has no solution mod p. 3

%I

%S 107,743,1061,1697,2333,2969,3181,3499,3923,4241,4877,5407,6043,6361,

%T 6679,6997,7103,7951,8269,8693,9011,9859,10177,10601,11131,12721,

%U 13463,13781,14629,14947,15053,15583,15901,16007,17491,17597,18127,18233

%N Primes p such that x^53 = 2 has no solution mod p.

%C Complement of A049585 relative to A000040.

%C Presumably this is also Primes congruent to 1 mod 53 (A212377). - _N. J. A. Sloane_, Jul 11 2008

%C Not so. The smallest counterexample is the prime 91373: 91373 == 1 (mod 53), but 2246^53 == 2 (mod 91373), therefore this prime is not in the sequence. - _Bruno Berselli_, Sep 20 2012

%H Vincenzo Librandi, <a href="/A059258/b059258.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_] := Reduce[Mod[x^53 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2500]], ok] (* _Vincenzo Librandi_, Sep 20 2012 *)

%o (MAGMA) [p: p in PrimesUpTo(20000) | not exists{x: x in ResidueClassRing(p) | x^53 eq 2}]; // _Vincenzo Librandi_, Sep 20 2012

%Y Cf. A000040, A049585, A212377.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Jan 23 2001

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Last modified May 11 03:49 EDT 2021. Contains 343784 sequences. (Running on oeis4.)