3 problems

For a positive integer $d$, let $M(d)$ denote the number of integer translations producing a multiplicatively dependent pair in the paper's normalization. Unique maximum-13 conject…

For a positive integer $d$, consider the equation … with integer parameters $g\geq 2$ and $1\leq x<y$. A solution is primitive when the relevant parameters satisfy the coprimality…

For distinct integers $a,b$, let a translation $t\in\mathbb{Z}$ be counted when the pair $(a+t,b+t)$ is multiplicatively dependent, meaning that there are integers $(m,n)\ne(0,0)$…