Let's call a pair of positive integers $(k,n)$ interesting if $n$ is composite and for every divisor $d<n$ of $n$ at least one of $d-k$ and $d+k$ is also a divisor of $n$ Find the number of interesting pairs $(k,n)$ with $k \leq 100$ M. Karpuk
Source: Belarusian national olympiad 2024
Tags: number theory
Let's call a pair of positive integers $(k,n)$ interesting if $n$ is composite and for every divisor $d<n$ of $n$ at least one of $d-k$ and $d+k$ is also a divisor of $n$ Find the number of interesting pairs $(k,n)$ with $k \leq 100$ M. Karpuk