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 A045316 Primes p such that x^8 = 2 has no solution mod p. 4

%I

%S 3,5,11,13,17,19,29,37,41,43,53,59,61,67,83,97,101,107,109,113,131,

%T 137,139,149,157,163,173,179,181,193,197,211,227,229,241,251,269,277,

%U 281,283,293,307,313,317,331,347,349,353,373,379,389

%N Primes p such that x^8 = 2 has no solution mod p.

%C Complement of A045315 relative to A000040. Coincides for the first 140 terms with the sequence of primes p such that x^16 = 2 has no solution mod p (first divergence is at 1217, cf. A059287) - _Klaus Brockhaus_, Jan 26 2001.

%H Vincenzo Librandi, <a href="/A045316/b045316.txt">Table of n, a(n) for n = 1..1000</a>

%t ok[p_]:= Reduce[Mod[x^8 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok] (* _Vincenzo Librandi_, Sep 19 2012 *)

%o (MAGMA) [p: p in PrimesUpTo(500) | not exists{x : x in ResidueClassRing(p) | x^8 eq 2} ]; // _Vincenzo Librandi_, Sep 19 2012

%Y Cf. A000040, A045315, A059287.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.

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Last modified May 16 02:39 EDT 2021. Contains 343937 sequences. (Running on oeis4.)