# A Simple Proof of Ljunggren’s Binomial Congruence

Chua Cheong Siong
The American Mathematical Monthly
Vol. 121, No. 2 (February), pp. 162-164
DOI: 10.4169/amer.math.monthly.121.02.162
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.02.162
Page Count: 3

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Abstract Let p > 3 be a prime, and let a and b be positive integers with a ≥ b. In this article, we give a simple proof of the congruence. \documentclass{article} \pagestyle{empty}\begin{document} $$\left(\begin{matrix} {pa}\\ {pb}\end{matrix}\right)\equiv \left(\begin{matrix}a\\ b\end{matrix}\right)\pmod{p^3}.$$ \end{document}