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MathNet 2016-part-01 — 184 problems (EN–VI) Question 146

Math Olympiad Vault · MathNet 2016-part-01 — 184 problems (EN–VI)

Question 146

Let $a$ and $b$ be positive integers such that $a!b!$ is a multiple of $a! + b!$.
Prove that $3a \ge 2b + 2$.