Question 1
Find all pairs $(a,b)$ of positive integers such that $a^3$ is a multiple of $b^2$ and $b-1$ is a multiple of $a-1$.
An integer $n$ is a multiple of an integer $m$ if $n=km$ for some integer $k$.
An integer $n$ is a multiple of an integer $m$ if $n=km$ for some integer $k$.