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Slovenia — National Math Olympiad

Algebra Difficulty 3.6 AMC 10/12 Find the answer Slovenia

How many pairs $(m, n)$ of positive integers satisfy the condition $\frac{3}{m} + \frac{2}{n} = 1$ ?

Pick one

Solution

Clearly $m > 3$ and $n > 2$ . Since $n$ decreases as $m$ increases $n$ , we see that the only possible solutions are $(m, n) \in \{(4, 8), (5, 5), (6, 4), (9, 3)\}$ .

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