A371554 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.

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

Offset

1,1

Comments

See A371553.

Links

Ben Whitmore, Table of n, a(n) for n = 1..95

Formula

x^5 + A371553(n)*x + a(n) is irreducible and solvable by radicals.

Example

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.

Mathematica

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]]

Crossrefs

For values of b see A371553.

Sequence in context: A037939 A040010 A169857 * A160330 A074175 A074174

Adjacent sequences: A371551 A371552 A371553 * A371555 A371556 A371557

Keyword

nonn

Author

Ben Whitmore, Mar 27 2024

Status

approved