x8+ax7+b=0

Simplest examples of irreducible and solvable by radicals octic trinomials, x⁸+ax⁷+b, where a and b are integers. Checked range: |a|, |b| ≤ 2990000. Excluded trivial cases where a or b are equal zero.

Basic notes:

- if x⁸+ax⁷+b=0 is solvable then x⁸-ax⁷+b=0 is too. More generally x⁸+ax⁷+b=0 is solvable if and only if x⁸+acx⁷+bc⁸=0 is solvable (c is non-zero rational number).

- if x⁸+ax⁷+b=0 is solvable then x⁸+(a/b)x+(1/b)=0 is too. And in more general: x⁸+(ac⁷/b)x+(c⁸/b)=0

The following file contains their factorization.