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2xy is perfect square and x^2 + y^2 is prime

Source: Dutch NMO 2020 p4

November 23, 2020
number theoryPerfect Squareprime

Problem Statement

Determine all pairs of integers (x,y)(x, y) such that 2xy2xy is a perfect square and x2+y2x^2 + y^2 is a prime number.
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