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2011^{2012} divides n! if 2011^{2011} divides n!

Source: 2011 Saudi Arabia Pre-TST February 3.1

January 1, 2022
number theorydividesdivisible

Problem Statement

Let nn be a positive integer such that 201120112011^{2011} divides n!n!. Prove that 201120122011^{2012} divides n!n! .
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