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MathNet 2017-part-01 — 176 problems (EN–VI) Question 57

Math Olympiad Vault · MathNet 2017-part-01 — 176 problems (EN–VI)

Question 57

Find all pairs $(x, y)$ of positive integers such that
$$
x^3 + y^3 = x^2 + 42xy + y^2.
$$