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A059642
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Primes p such that x^55 = 2 has no solution mod p.
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2
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11, 23, 31, 41, 61, 67, 71, 89, 101, 131, 181, 191, 199, 211, 271, 281, 311, 331, 353, 397, 401, 419, 421, 461, 463, 491, 521, 541, 601, 617, 631, 661, 683, 691, 701, 727, 751, 761, 811, 821, 859, 881, 941, 947, 991, 1021, 1031, 1051, 1061, 1091, 1123
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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^55 - 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(1150) | not exists{x: x in ResidueClassRing(p) | x^55 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, 55), 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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