Let $n\geq 1$ be an integer and let $a$ and $b$ be its positive divisors satisfying $a+b+ab=n$. Prove that $a=b$.
Problem
Source: 2022 Polish Junior Math Olympiad Second Round
Tags: Chinese Remainder Theorem, matchings
Source: 2022 Polish Junior Math Olympiad Second Round
Tags: Chinese Remainder Theorem, matchings
Let $n\geq 1$ be an integer and let $a$ and $b$ be its positive divisors satisfying $a+b+ab=n$. Prove that $a=b$.