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Applications of mathematics for the design and analysis of games and puzzles

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While solving the 1988 IMO problem 6, I have questions about new solutions without using Vie... [closed]

I think most of you may know the well-known problem: "Let $x$ and $y$ be positive integers such that $xy + 1$ divides $x^{2} + y^{2}$. Show that $\frac {x^{2} + y^{2}}{xy + 1}$ is the perfect square." …
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