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A059643
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Primes p such that x^57 = 2 has no solution mod p.
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2
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7, 13, 19, 37, 61, 67, 73, 79, 97, 103, 139, 151, 163, 181, 191, 193, 199, 211, 229, 241, 271, 313, 331, 337, 349, 367, 373, 379, 409, 419, 421, 457, 463, 487, 523, 541, 547, 571, 577, 607, 613, 619, 631, 647, 661, 673, 709, 751, 757, 761, 769, 787, 823, 829
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OFFSET
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1,1
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COMMENTS
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LINKS
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MATHEMATICA
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ok[p_] := Reduce[Mod[x^57 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[200]], ok] (* Vincenzo Librandi, Sep 21 2012 *)
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PROG
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(Magma) [p: p in PrimesUpTo(900) | not exists{x: x in ResidueClassRing(p) | x^57 eq 2}]; // Vincenzo Librandi, Sep 21 2012
(PARI)
N=10^4; default(primelimit, N);
ok(p, r, k)={ return ( (p==r) || (Mod(r, p)^((p-1)/gcd(k, p-1))==1) ); }
forprime(p=2, N, if (! ok(p, 2, 57), print1(p, ", ")));
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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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