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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