What Are x and y?

One day, I give you the diophantine equation (x^2 + 1)(y^2 + 1) + 2(x − y)(1 − xy) = 4(1 + xy), can you find all integral solutions x and y that satisfies this diophantine equation? Give this problem a try and this problem comes from the book, ”An Introduction to Diophantine Equations” by Titu Andreescu. This is also a nice Number Theory Warm-Up!
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"An Introduction to Diophantine Equations" by Titu Andreescu
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