论文标题
Lucas的定理Modulo $ P^2 $
Lucas' theorem modulo $p^2$
论文作者
论文摘要
卢卡斯定理描述了如何减少二项式系数$ \ binom {a} {b} $ modulo $ p $，通过打破最不重要的数字为$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $和$ b $。我们表征了卢卡斯定理保留Modulo $ p^2 $的这些数字对。这种表征是使用帕斯卡三角形的对称性自然表达的。
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.
