Note on a Binomial Coefficient Divisor

Summary

Let n be a positive integer, and k and integer with $0\le k\le n$. Let g be the greatest common divisor of k and n. We use the cycle construction to give a combinatorial proof that the fraction n/g divides the binomial coefficient $(\begin{array}{c}n\\ k\end{array})$.

MSC:

• Primary 05A10
• Secondary 11A05

Acknowledgments

The author was partially supported by the Research and Training Group grant DMS-1344994 funded by the National Science Foundation. He thanks Madeline Dawsey, Paul Pollack, Robert Schneider, and an anonymous referee for helpful comments.

Additional information

Notes on contributors

Matthew Just

MATTHEW JUST teaches at the University of Georgia in Athens. He enjoys spending time with his family, playing duplicate bridge, and showing others the joy of mathematics.