# Like Base System?

Number Theory Level pending

For each integer $$n\geq 4$$, let $$a_n$$ denote the base-$$n$$ number $$(0.133133133\ldots)_n$$. The product $$a_4a_5\cdots a_{99}$$ can be expressed as $$\dfrac{m}{n!}$$, where $$m$$ and $$n$$ are positive integers and $$n$$ is as small as possible. What is the value of $$m$$?

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