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product of n consecutives = product of n + 100 consecutives

Source: All-Russian MO 2009 Regional 10. 2

August 27, 2024
number theoryconsecutiveProduct

Problem Statement

Prove that there is a natural number n>1n > 1 such that the product of some nn consecutive natural numbers is equal to the product of some n+100n + 100 consecutive natural numbers.
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