x8+ax5+b=0

Simplest examples of irreducible and solvable by radicals octic trinomials, x⁸+ax⁵+b, where a and b are integers. Checked range: |a|, |b| ≤ 7,900,000. Excluded trivial cases where a or b are equal zero.

Basic notes:

- if x⁸+ax⁵+b=0 is solvable then x⁸-ax⁵+b=0 is too. More generally x⁸+ax⁵+b=0 is solvable if and only if x⁸+ac³x⁵+bc⁸=0 is solvable (c is non-zero rational number).

- if x⁸+ax⁵+b=0 is solvable then x⁸+(a/b)x³+(1/b)=0 is too. And in more general: x⁸+(ac⁵/b)x³+(c⁸/b)=0

The following file contains its factorization.