Izadi–Baghalaghdam conjectural extension to all rational parameters

Establish whether the quartic Diophantine equation A^4 + a B^4 = C^4 + a D^4 is solvable for every rational parameter a ∈ Q.

Background

In discussing a variant of formulation (B), the paper cites Izadi and Baghalaghdam (2017) and notes their extension of the conjectured solvability domain from integers to all rationals.

This frames a broader conjectural claim about solvability for every rational a, beyond the natural numbers considered in most computational tables.