Where are the numbers?

True or False:

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

Notation: !! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .


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