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a,b relative prime and divide x^3 + y^3 => (a+b - 1) divides (x^3+y^3)

Source: Balkan BMO Shortlist 2015 N4

August 5, 2019
number theoryrelatively primeDivisibility

Problem Statement

Find all pairs of positive integers (x,y)(x,y) with the following property: If a,ba,b are relative prime and positive divisors of x3+y3 x^3 + y^3, then a+bāˆ’1a+b - 1 is divisor of x3+y3x^3+y^3.
(Cyprus)
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