Let a,b and n be positive integers with a>b such that all of the following hold:i. a2021 divides n,
ii. b2021 divides n,
iii. 2022 divides aāb. 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 20222.Proposed by Silouanos Brazitikos, Greece number theoryBalkan Mathematics OlympiadDivisors