39th Balkan Mathematical Olympiad (BMO 2022 )


Problem 2 Let $a, b$ and $n$ be positive integers with $a>b$ such that all of the following hold: i. $a^{2021}$ divides $n$ , ii. $b^{2021}$ divides $n$ , iii. 2022 divides $a-b$ . Prove that there is a subset $T$ of the set of positive divisors of the number $n$ such that the sum of the elements of $T$ is divisible by 2022 but not divisible by $2022^2$ .



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