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A212376
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Primes p such that x^48 = 2 has no solution mod p.
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3
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3, 5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 73, 79, 83, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 193, 197, 199, 211, 227, 229, 241, 251, 269, 271, 277, 281, 283, 293, 307, 313, 317, 331, 337, 347, 349, 353, 367
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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 A059362. First disagreement at index 162: a(162)=1217, A059362(162)=1229.
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LINKS
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MATHEMATICA
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Select[Prime[Range[PrimePi[400]]], ! MemberQ[PowerMod[Range[#], 48, #], Mod[2, #]] &]
ok[p_] := Reduce[Mod[x^48 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[75]], ok] (* Vincenzo Librandi, Sep 21 2012 *)
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PROG
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(Magma) [p: p in PrimesUpTo(400) | forall{x: x in ResidueClassRing(p) | x^48 ne 2}];
(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, 48), 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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