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Diophantine Equation with gcd+lcm

Source: Cyprus 2021Junior TST-2 Problem 2

May 26, 2021
number theoryDiophantine equationGCDLCM

Problem Statement

Find all pairs of natural numbers (α,β)(\alpha,\beta) for which, if δ\delta is the greatest common divisor of α,β\alpha,\beta, and Δ\varDelta is the least common multiple of α,β\alpha,\beta, then δ+Δ=4(α+β)+2021 \delta + \Delta = 4(\alpha + \beta) + 2021
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