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A240583
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Odd primes satisfying a specific condition (see comments).
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2
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47, 79, 167, 191, 223, 239, 263, 359, 367, 383, 431, 439, 463, 479, 503, 599, 607, 719, 823, 839, 863, 887, 911, 983, 1031, 1039, 1087, 1103, 1223, 1231, 1303, 1319, 1327, 1367, 1399, 1439, 1447, 1487, 1511, 1543, 1559, 1583, 1663, 1759, 1823, 1831, 1847
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OFFSET
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1,1
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COMMENTS
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Condition on odd prime p so that Q(Cp) is not rational over Q: p = 2q+1 where q = -1 (mod 4), q is squarefree, and any of 4p-q and q+1 is not square.
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LINKS
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MATHEMATICA
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Select[Prime[Range[2, 300]], (q = (#-1)/2; SquareFreeQ[q] && Mod[q, 4] == 3 && !IntegerQ[Sqrt[4#-q]] && !IntegerQ[Sqrt[q+1]])&] (* Jean-François Alcover, Sep 22 2018 *)
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PROG
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(PARI) isok(p) = isprime(p) && ((q = (p-1)/2) && issquarefree(q) && ((q % 4) == 3) && (!issquare(4*p-q)));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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