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MathNet 2015-part-02 — 191 problems (EN–VI) Question 144

Math Olympiad Vault · MathNet 2015-part-02 — 191 problems (EN–VI)

Question 144

A positive integer $n$ is interesting, if for some positive integer $m$ and positive integers $a$, $b$ that are smaller than $m$, $\frac{m^2}{ab} = n$. For example, $10$ is interesting because $\frac{20^2}{4 \cdot 10} = 10$. Find the smallest interesting integer.