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Found problems: 1

2022 All-Russian Olympiad, 1
Tags: divisor , all russia mo , number theory
We call the $main$ $divisors$ of a composite number $n$ the two largest of its natural divisors other than $n$. Composite numbers $a$ and $b$ are such that the main divisors of $a$ and $b$ coincide. Prove that $a=b$.