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BMO 2021 problem 3

Source: Balkan MO 2021 P3

September 8, 2021
number theory

Problem Statement

Let a,ba, b and cc be positive integers satisfying the equation (a,b)+[a,b]=2021c(a, b) + [a, b]=2021^c. If ∣a−b∣|a-b| is a prime number, prove that the number (a+b)2+4(a+b)^2+4 is composite.
Proposed by Serbia
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