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A042966
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Primes p such that x^7 = 2 has a solution mod p.
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11
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2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 37, 41, 47, 53, 59, 61, 67, 73, 79, 83, 89, 97, 101, 103, 107, 109, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 199, 223, 227, 229, 233, 241, 251, 257, 263, 269, 271, 277, 283, 293, 307, 311, 313, 317, 331
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OFFSET
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1,1
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COMMENTS
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Coincides with sequence of "primes p such that x^49 = 2 has a solution mod p" for first 572 terms, then diverges.
a(98) = 631 is the first such prime that is congruent to 1 (mod 7). - Georg Fischer, Jan 06 2022
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LINKS
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MATHEMATICA
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ok[p_]:= Reduce[Mod[x^7 - 2, p] == 0, x, Integers]=!=False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 13 2012 *)
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PROG
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(Magma) [p: p in PrimesUpTo(400) | exists{x: x in ResidueClassRing(p) | x^7 eq 2}]; // Bruno Berselli, Sep 12 2012
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CROSSREFS
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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, ...
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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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