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a^2(b-a)/(b+a) is perfect square of a prime

Source: Mathematics Regional Olympiad of Mexico West 2019 P3

September 9, 2022
number theoryPerfect Square

Problem Statement

Determine all pairs (a,b)(a,b) of natural numbers such that the number a2(b−a)b+a\frac{a^2(b-a)}{b+a} is the square of a prime number.
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