MathDB
Powerful Sets

Source: Balkan MO 2022 P2

May 6, 2022
number theoryBalkan Mathematics OlympiadDivisors

Problem Statement

Let a,ba, b and nn be positive integers with a>ba>b such that all of the following hold:
i. a2021a^{2021} divides nn, ii. b2021b^{2021} divides nn, iii. 2022 divides aāˆ’ba-b.
Prove that there is a subset TT of the set of positive divisors of the number nn such that the sum of the elements of TT is divisible by 2022 but not divisible by 202222022^2.
Proposed by Silouanos Brazitikos, Greece
Back to ProblemsView on AoPS