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PAMO 2022 Problem 2 - Three expressions are all squares

Source: 2022 Pan-African Mathematics Olympiad Problem 2

June 25, 2022
number theoryalgebraPerfect Squares

Problem Statement

Find all 33-tuples (a,b,c)(a, b, c) of positive integers, with a≥b≥ca \geq b \geq c, such that a2+3ba^2 + 3b, b2+3cb^2 + 3c, and c2+3ac^2 + 3a are all squares.
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