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arXiv · 2006.11701

Lucas' theorem modulo $p^2$

Eric Rowland
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Abstract

Lucas' theorem describes how to reduce a binomial coefficient $\binom{a}{b}$ modulo $p$ by breaking off the least significant digits of $a$ and $b$ in base $p$. We characterize the pairs of these digits for which Lucas' theorem holds modulo $p^2$. This characterization is naturally expressed using symmetries of Pascal's triangle.

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Eric Rowland. 2020-06-21. Lucas' theorem modulo $p^2$. https://doi.org/10.1080/00029890.2022.2038004

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