OFFSET
1,1
LINKS
Ben Whitmore, Table of n, a(n) for n = 1..67
FORMULA
x^5 + A371557(n)*x + a(n) is irreducible and solvable by radicals.
EXAMPLE
a(1) = 12 because A371557(1) = -5, and x^5 - 5*x + 12 is irreducible and solvable by radicals, and (-5, 12) is a primitive pair.
MATHEMATICA
pairs = Join @@ Table[
Select[{b, 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, -1}
];
pairs[[All, 2]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ben Whitmore, Apr 22 2024
STATUS
approved