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MathNet 2019-part-07 — 184 problems (EN–VI) Question 128

Math Olympiad Vault · MathNet 2019-part-07 — 184 problems (EN–VI)

Question 128

Find all pairs of positive integers $(a, b)$ which satisfy the equation:
$$
ab^3 + a^3 + b + 1 = 2019.
$$