# Where are the numbers?

True or False:

Suppose there is a positive integer $$a$$ such that $$a!$$ has $$m$$ trailing number of zeros. There is another distinct positive integer $$b$$ such that $$b!$$ has $$n$$ trailing number of zeros. Then, $$(a+b)!$$ must have $$m+n$$ trailing number of zeros.

Notation: $$!$$ denotes the factorial notation. For example, $$8! = 1\times2\times3\times\cdots\times8$$.

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