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Number theory

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If m is the smallest positive integer such that m! is a multiple of 4125, and n is the smallest positive integer such that n! is a multiple of 2816000, then find n-m.

Oct 21, 2021

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Hello,

m and n can only be bigger than 4125 or 2816000,

$$m=15$$ $$\frac{15!}{4125}=317011968$$ and

$$n=15$$ $$\frac{15!}{2816000}=464373$$ .

n is also 15.

Straight

Oct 21, 2021
edited by Straight  Oct 21, 2021