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MathNet 2019-part-01 — 184 problems (EN–VI) Question 25

Math Olympiad Vault · MathNet 2019-part-01 — 184 problems (EN–VI)

Question 25

Let $x$ and $y$ be integers for which $x + y \neq 0$ holds. Determine all pairs $(x, y)$ satisfying
$$
\frac{x^2 + y^2}{x + y} = 10.
$$