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 A040098 Primes p such that x^4 = 2 has a solution mod p. 23
 2, 7, 23, 31, 47, 71, 73, 79, 89, 103, 113, 127, 151, 167, 191, 199, 223, 233, 239, 257, 263, 271, 281, 311, 337, 353, 359, 367, 383, 431, 439, 463, 479, 487, 503, 577, 593, 599, 601, 607, 617, 631, 647, 719, 727, 743, 751, 823, 839, 863, 881, 887, 911, 919 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 Complement of A040100 relative to A000040. - Vincenzo Librandi, Sep 13 2012 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 Franz Lemmermeyer, Bibliography on Reciprocity Laws MATHEMATICA ok[p_] := Reduce[ Mod[x^4 - 2, p] == 0, x, Integers] =!= False; Select[ Prime[ Range[200]], ok] (* Jean-François Alcover, Dec 14 2011 *) PROG (MAGMA) [ p: p in PrimesUpTo(919) | exists(t){x : x in ResidueClassRing(p) | x^4 eq 2} ]; // Klaus Brockhaus, Dec 02 2008 (PARI) forprime(p=2, 2000, if([]~!=polrootsmod(x^4-2, p), print1(p, ", "))); print(); \\ Joerg Arndt, Jul 27 2011 CROSSREFS Cf. A000040, A001132, A040028, A040100, A045315. 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, ... Sequence in context: A042145 A309580 A186098 * A045315 A072935 A049564 Adjacent sequences:  A040095 A040096 A040097 * A040099 A040100 A040101 KEYWORD nonn,nice,easy AUTHOR STATUS approved

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Last modified September 26 11:29 EDT 2020. Contains 337367 sequences. (Running on oeis4.)