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%I #27 Feb 21 2022 01:05:48
%S 2,7,23,31,47,71,73,79,89,103,113,127,151,167,191,199,223,233,239,257,
%T 263,271,281,311,337,353,359,367,383,431,439,463,479,487,503,577,593,
%U 599,601,607,617,631,647,719,727,743,751,823,839,863,881,887,911,919
%N Primes p such that x^4 = 2 has a solution mod p.
%C For a prime p congruent to 1 mod 8, 2 is a biquadratic residue mod p if and only if there are integers x,y such that x^2 + 64*y^2 = p. 2 is also a biquadratic residue mod 2 and mod p for any prime p congruent to 7 mod 8 and for no other primes. - Fred W. Helenius (fredh(AT)ix.netcom.com), Dec 30 2004
%C Complement of A040100 relative to A000040. - _Vincenzo Librandi_, Sep 13 2012
%H T. D. Noe, <a href="/A040098/b040098.txt">Table of n, a(n) for n = 1..1000</a>
%H Franz Lemmermeyer, <a href="http://www.rzuser.uni-heidelberg.de/~hb3/recbib.html">Bibliography on Reciprocity Laws</a>
%H <a href="/index/Pri#smp">Index entries for related sequences</a>
%t ok[p_] := Reduce[ Mod[x^4 - 2, p] == 0, x, Integers] =!= False; Select[ Prime[ Range[200]], ok] (* _Jean-François Alcover_, Dec 14 2011 *)
%o (Magma) [ p: p in PrimesUpTo(919) | exists(t){x : x in ResidueClassRing(p) | x^4 eq 2} ]; // _Klaus Brockhaus_, Dec 02 2008
%o (PARI) forprime(p=2,2000,if([]~!=polrootsmod(x^4-2,p),print1(p,", ")));print(); \\ _Joerg Arndt_, Jul 27 2011
%Y Cf. A000040, A001132, A040028, A040100, A045315.
%Y For primes p such that x^m == 2 mod p has a solution for m = 2,3,4,5,6,7,... see A038873, A040028, A040098, A040159, A040992, A042966, ...
%K nonn,nice,easy
%O 1,1
%A _N. J. A. Sloane_
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