Mock AIME 5 2005-2006 Problems/Problem 4

Problem

Let $m$ and $n$ be integers such that $1 < m \le 10$ and $m < n \le 100$ . Given that $x = \log_m{n}$ and $y = \log_n{m}$ , find the number of ordered pairs $(m,n)$ such that $\lfloor x \rfloor = \lceil y \rceil$ . ( $\lfloor a \rfloor$ is the greatest integer less than or equal to $a$ and $\lceil a \rceil$ is the least integer greater than or equal to $a$ ).

Mock AIME 5 2005-2006 (Problems, Source)
Preceded by Problem 3	Followed by Problem 5
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Mock AIME 5 2005-2006 Problems/Problem 4

Problem

Solution

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