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A371554
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Consider primitive pairs of integers (b, c) with b > 0 such that x^5 + b*x + c = 0 is irreducible and solvable by radicals: sequence gives values of c.
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2
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44, 12, 44, 32, 64, 1344, 576, 1344, 832, 275, 4170, 2375, 3750, 4060, 128700, 13243, 1510620, 24000, 3348800, 8788, 467961, 51072, 133440, 474214, 61500, 128700, 85683, 514098, 509197, 199927, 24000, 3720000, 21376538, 210990, 486343, 114244, 12681084
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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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FORMULA
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x^5 + A371553(n)*x + a(n) is irreducible and solvable by radicals.
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EXAMPLE
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a(1) = 44 because A371553(1) = 11, and x^5 + 11*x + 44 is irreducible and solvable by radicals, and (11, 44) is a primitive pair.
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MATHEMATICA
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pairs = Join @@ Table[
Select[{m, Abs[#1 - b] #2/5} & @@@
Sort[SolveValues[x^2 - (6b + 5y^4)x + 25b^2 == 0 && y > 0, {x, y},
Integers]],
Max[Last /@ FactorInteger[GCD @@ #]] < 4 &&
AllTrue[#, IntegerQ] &&
IrreduciblePolynomialQ[x^5 + #1x + #2 & @@ #] &
],
{b, 1, 1000}
];
pairs[[All, 2]]
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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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