by henderson, Feb 12, 2016, 6:21 PM 
Prove that for all integers 
![\[\frac{\gcd(m,n)}{n}\cdot\binom{n}{m}\]](http://latex.artofproblemsolving.com/1/0/7/1072bd1a426e48ea92c7cc0852f4161319fa9061.png)
is an integer.
There exist integers 
such that 
![\[ \frac{gcd(m,n)}{n} \binom{n}{m}=a\frac{m}{n}\binom{n}{m} +b\binom{n}{m}=a\binom{n-1}{m-1} +b\binom{n}{m}.\]](http://latex.artofproblemsolving.com/7/e/e/7ee91e40296d93efc24c1fc7e4b32e02d0583cbf.png)
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