MathDB

1

Part of 2021 Irish Math Olympiad

Problems(1)

15! as product of 9 different integers

Source: 2021 Irish Mathematical Olympiad P1

5/30/2021
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.
number theoryfactorial