2019-02 Simplification of an expression with factorials

For any positive integers m and n, show that

\[ C_{n,m} = \frac{(mn)!}{(m!)^n n!} \] is an integer.

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About Hyungryul

2003.3-2009.8 KAIST, Undergraduate student in Mathematics 2009.8-2014.8 Cornell University, PhD student in Mathematics 2014.9-2017.2 University of Bonn, Postdoc 2017.3-2021.2. KAIST, Assistant Professor 2021.3-Present. KAIST, Associate Professor