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%I #17 Aug 08 2019 11:05:36
%S 4421,4733,5669,5981,8581,9413,10453,11597,13963,14327,14951,19267,
%T 22699,22907,23557,25117,25819,26417,28627,31799,32579,35491,37441,
%U 41549,44773,44851,45553,46619,46957,48179,49297,49921,49999,50207,52859,53639,60217,64403
%N Primes p congruent to 1 modulo 13 such that x^13 = 2 has a solution modulo p.
%C Intersection of A049545 and A268753.
%C These are the counterexamples mentioned in the Sep 12 2012 comment from _Bruno Berselli_ in A059245.
%e 4421 is in the sequence since it is prime, it is congruent to 1 (mod 13), and x^13 == 2 (mod 4421) has the solution x = 162. - _Michael B. Porter_, Aug 26 2016
%t Quiet@ Select[Prime@ Range[10^4], And[Mod[#, 13] == 1, IntegerQ@ PowerMod[2, 1/13, #]] &] (* _Michael De Vlieger_, Aug 10 2016 *)
%o (PARI) forprime(p=1, 1e6, if(Mod(p, 13)==1 && ispower(Mod(2, p), 13), print1(p, ", ")))
%Y Cf. A049545, A059245, A268753.
%K nonn
%O 1,1
%A _Felix Fröhlich_, Aug 08 2016
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