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MathNet 2019-part-06 — 184 problems (EN–VI) Question 153

Math Olympiad Vault · MathNet 2019-part-06 — 184 problems (EN–VI)

Question 153

Find all pairs of integers $(x, y)$ such that
$$
3^4 2^3 (x^2 + y^2) = x^3 y^3.
$$