MathDB

Ratio of Factorials

Source: 2016 USAMO 2

April 19, 2016

factorial2016 USAMO2016 USAMO Problem 2USAMOUSA(J)MOAMC

Problem Statement

Prove that for any positive integer

k

(k^2)!\cdot\displaystyle\prod_{j=0}^{k-1}\frac{j!}{(j+k)!}

is an integer.