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A040098
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Primes p such that x^4 = 2 has a solution mod p.
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19
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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; internal format)
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OFFSET
| 1,1
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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
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Franz Lemmermeyer, Bibliography on Reciprocity Laws
Index entries for related sequences
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MATHEMATICA
| ok[p_] := Reduce[ Mod[x^4 - 2, p] == 0, x, Integers] =!= False; Select[ Prime[ Range[200]], ok] (* From Jean-François Alcover, Dec 14 2011 *)
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PROG
| (MAGMA) [ p: p in PrimesUpTo(919) | exists(t){x : x in ResidueClassRing(p) | x^4 eq 2} ]; [From Klaus Brockhaus, Dec 02 2008]
(PARI) forprime(p=2, 2000, if([]~!=polrootsmod(x^4-2, p), print1(p, ", "))); print();
/* Joerg Arndt, Jul 27 2011 */
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CROSSREFS
| Cf. A001132, A040028, A045315.
Sequence in context: A180537 A042145 A186098 * A045315 A072935 A049564
Adjacent sequences: A040095 A040096 A040097 * A040099 A040100 A040101
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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