Very Difficult Roots of Unity Filter

by HKIS200543, Aug 16, 2017, 12:25 AM

Problem: (AMSP NT3) Let $p$ be a prime and $n$, $s$ positive integers. Prove that $p^q$ divides
\[ \sum_{\substack{0 \leq k \leq n\\ p \mid k-s}} (-1)^k \binom{n}{k} \]where $q= \left\lfloor{\frac{n-1}{p-1}}\right\rfloor$

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This post has been edited 3 times. Last edited by HKIS200543, Aug 30, 2017, 10:37 AM

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Why do you use $p^q.x.A$ instead of $p^q\cdot x\cdot A$?

by pinetree1, Sep 3, 2017, 4:29 PM

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