An integer $ n>101$ is divisible by $ 101$. Suppose that every divisor $ d$ of $ n$ with $ 1<d<n$ equals the difference of two divisors of $ n$. Prove that $ n$ is divisble by $ 100$.
Source: Ukraine 2005 grade 10
Tags: number theory unsolved, number theory
An integer $ n>101$ is divisible by $ 101$. Suppose that every divisor $ d$ of $ n$ with $ 1<d<n$ equals the difference of two divisors of $ n$. Prove that $ n$ is divisble by $ 100$.