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Problem of the Week # 266 - Jun 05, 2017

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Ackbach

Indicium Physicus
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Jan 26, 2012
4,198
Here is this week's POTW:

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Prove that the expression
\[ \frac{\gcd(m,n)}{n}\binom{n}{m} \]
is an integer for all pairs of integers $n\geq m\geq 1$.

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Remember to read the POTW submission guidelines to find out how to submit your answers!
 
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Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,198
Re: Problem Of The Week # 266 - Jun 05, 2017

This was Problem B-2 in the 2000 William Lowell Putnam Mathematical Competition.

Congratulations to joypav for his correct solution, which follows:

 
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