Difference between revisions of "1972 IMO Problems/Problem 3"
| Line 1: | Line 1: | ||
| − | Let m and n be arbitrary non-negative integers. Prove that | + | Let <math>m</math> and <math>n</math> be arbitrary non-negative integers. Prove that |
| − | + | <cmath>\frac{(2m)!(2n)!}{m!n!(m+n)!}</cmath> | |
| − | < | + | is an integer. (<math>0! = 1</math>.) |
| − | |||
| − | is an integer. (0! = 1.) | ||
== Solution == | == Solution == | ||
Revision as of 16:38, 17 October 2014
Let 
and 
be arbitrary non-negative integers. Prove that
![\[\frac{(2m)!(2n)!}{m!n!(m+n)!}\]](http://latex.artofproblemsolving.com/3/2/3/323dce2539f7ac15a9beb292b765590b9cf1f5ad.png)
is an integer. (
.)
