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MathNet 2019-part-07 — 184 problems (EN–VI) Question 134

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

Question 134

Find all triples of positive integers $(m, n, k)$ that satisfy the equation
$$
(m! + m)(n! + n) = (k! + k).
$$