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A212375
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Primes p such that x^18 = 2 has no solution mod p.
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2
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3, 5, 7, 11, 13, 19, 29, 37, 43, 53, 59, 61, 67, 73, 79, 83, 97, 101, 103, 107, 109, 131, 139, 149, 151, 157, 163, 173, 179, 181, 193, 197, 199, 211, 227, 229, 241, 251, 269, 271, 277, 283, 293, 307, 313, 317, 331, 337, 347, 349, 367, 373, 379, 389, 397
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OFFSET
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1,1
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COMMENTS
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This sequence is not the same as A040993. First disagreement at index 59: a(59)=433, A040993(59)=443.
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LINKS
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MATHEMATICA
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Select[Prime[Range[PrimePi[500]]], ! MemberQ[PowerMod[Range[#], 18, #], Mod[2, #]] &]
ok[p_]:= Reduce[Mod[x^18 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[80]], ok] (* Vincenzo Librandi, Sep 20 2012 *)
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PROG
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(Magma) [p: p in PrimesUpTo(500) | forall{x: x in ResidueClassRing(p) | x^18 ne 2}];
(Magma) [p: p in PrimesUpTo(400) | not exists{x : x in ResidueClassRing(p) | x^18 eq 2} ]; // Vincenzo Librandi, Sep 20 2012
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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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STATUS
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approved
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