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A045315 Primes p such that x^8 = 2 has a solution mod p.

%I A045315 #31 Feb 21 2022 01:04:56
%S A045315 2,7,23,31,47,71,73,79,89,103,127,151,167,191,199,223,233,239,257,263,
%T A045315 271,311,337,359,367,383,431,439,463,479,487,503,599,601,607,631,647,
%U A045315 719,727,743,751,823,839,863,881,887,911,919,937,967,983,991,1031,1039
%N A045315 Primes p such that x^8 = 2 has a solution mod p.
%C A045315 Coincides with the sequence of "primes p such that x^16 = 2 has a solution mod p" for first 58 terms (and then diverges).
%C A045315 Complement of A045316 relative to A000040. - _Vincenzo Librandi_, Sep 13 2012
%D A045315 A. Aigner, Kriterien zum 8. und 16. Potenzcharakter der Reste 2 und -2, Deutsche Math. 4 (1939), 44-52; FdM 65 - I (1939), 112.
%H A045315 T. D. Noe, <a href="/A045315/b045315.txt">Table of n, a(n) for n = 1..1000</a>
%H A045315 H. Hasse, <a href="https://doi.org/10.1007/BF02854527">Der 2^n-te Potenzcharakter von 2 im Koerper der 2^n-ten Einheitswurzeln</a>, Rend. Circ. Matem. Palermo (2), 7 (1958), 185-243.
%H A045315 Franz Lemmermeyer, <a href="http://www.rzuser.uni-heidelberg.de/~hb3/recbib.html">Bibliography on Reciprocity Laws</a>
%H A045315 A. L. Whiteman, <a href="http://dx.doi.org/10.4153/CJM-1954-035-8">The sixteenth power residue character of 2</a>, Canad. J. Math. 6 (1954), 364-373; Zbl 55.27102.
%H A045315 <a href="/index/Pri#smp">Index entries for related sequences</a>
%t A045315 ok[p_] := Reduce[ Mod[x^8-2, p] == 0, x, Integers] =!= False; Select[ Prime[ Range[200] ], ok] (* _Jean-François Alcover_, Nov 28 2011 *)
%o A045315 (Magma) [p: p in PrimesUpTo(1100) | exists(t){x : x in ResidueClassRing(p) | x^8 eq 2}]; // _Vincenzo Librandi_, Sep 13 2012
%o A045315 (PARI) is(n)=isprime(n) && ispower(Mod(2,n),8) \\ _Charles R Greathouse IV_, Feb 08 2017
%Y A045315 Cf. A000040, A001132, A040028, A040098, A045316.
%K A045315 nonn,easy,nice
%O A045315 1,1
%A A045315 _N. J. A. Sloane_