2 problems

Let $a,b\geqslant 2$ be integers, and choose maximal positive integers $k$ and $\ell$ such that $a=A^k$ and $b=B^\ell$. Granville–Pappalardi's power-base conjecture. There are infi…

Let $a,b\geqslant 2$ be integers. Say that there is no obstruction when neither $a$ nor $b$ is a power of an integer and there is no non-zero integer $Q$ such that … for all positi…