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A049580
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Primes p such that x^48 = 2 has a solution mod p.
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3
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2, 23, 31, 47, 71, 89, 127, 167, 191, 223, 233, 239, 257, 263, 311, 359, 383, 431, 439, 479, 503, 599, 601, 647, 719, 727, 743, 839, 863, 881, 887, 911, 919, 983, 1031, 1103, 1151, 1223, 1289, 1319, 1327, 1367, 1399, 1423, 1433, 1439, 1471, 1487, 1511, 1559
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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^48 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[300]], ok] (* Vincenzo Librandi, Sep 14 2012 *)
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PROG
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(Magma) [p: p in PrimesUpTo(1600) | exists(t){x : x in ResidueClassRing(p) | x^48 eq 2}]; // Vincenzo Librandi, Sep 14 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, 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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