Prove that there is a natural number $n > 1$ such that the product of some $n$ consecutive natural numbers is equal to the product of some $n + 100$ consecutive natural numbers.
Source: All-Russian MO 2009 Regional 10. 2
Tags: number theory, consecutive, Product
Prove that there is a natural number $n > 1$ such that the product of some $n$ consecutive natural numbers is equal to the product of some $n + 100$ consecutive natural numbers.