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A040034
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Primes p such that x^3 = 2 has no solution mod p.
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5
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7, 13, 19, 37, 61, 67, 73, 79, 97, 103, 139, 151, 163, 181, 193, 199, 211, 241, 271, 313, 331, 337, 349, 367, 373, 379, 409, 421, 463, 487, 523, 541, 547, 571, 577, 607, 613, 619, 631, 661, 673, 709, 751, 757, 769, 787, 823, 829, 853, 859, 877, 883, 907, 937
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OFFSET
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1,1
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COMMENTS
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Primes represented by the quadratic form 4x^2 + 2xy + 7y^2, whose discriminant is -108. - T. D. Noe, May 17 2005
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LINKS
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EXAMPLE
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A cube modulo 7 can only be 0, 1 or 6, but not 2, hence the prime 7 is in the sequence.
Because x^3 = 2 mod 11 when x = 7 mod 11, the prime 11 is not in the sequence.
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MATHEMATICA
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insolublePrimeQ[p_]:= Reduce[Mod[x^3 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[200]], insolublePrimeQ] (* Vincenzo Librandi Sep 17 2012 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(937) | forall(t){x : x in ResidueClassRing(p) | x^3 ne 2} ]; // Klaus Brockhaus, Dec 05 2008
(PARI) forprime(p=2, 10^3, if(#polrootsmod(x^3-2, p)==0, print1(p, ", "))) \\ Joerg Arndt, Jul 16 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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