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15! as product of 9 different integers

Source: 2021 Irish Mathematical Olympiad P1

May 30, 2021
number theoryfactorial

Problem Statement

Let N=15!=15⋅14⋅13...3⋅2⋅1N = 15! = 15\cdot 14\cdot 13 ... 3\cdot 2\cdot 1. Prove that NN can be written as a product of nine different integers all between 1616 and 3030 inclusive.
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