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a^2 + b^2 divides both a^3 + 1 and b^3 + 1

Source: 2013 Saudi Arabia GMO TST III p4

July 26, 2020
number theorydividesdivisible

Problem Statement

Find all pairs of positive integers (a,b)(a,b) such that a2+b2a^2 + b^2 divides both a3+1a^3 + 1 and b3+1b^3 + 1.
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