MathDB

3

Part of 2018 Cono Sur Olympiad

Problems(1)

Third problem

Source: Cono Sur Olympiad 2018 #3

8/27/2018
Define the product Pn=1!⋅2!⋅3!⋯(n−1)!⋅n!P_n=1! \cdot 2!\cdot 3!\cdots (n-1)!\cdot n! a) Find all positive integers mm, such that P2020m!\frac {P_{2020}}{m!} is a perfect square. b) Prove that there are infinite many value(s) of nn, such that Pnm!\frac {P_{n}}{m!} is a perfect square, for at least two positive integers mm.
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