Congruences involving $\binom{4k}{2k}$ and $\binom{3k}k$

Details Congruences involving $\binom{4k}{2k}$ and $\binom{3k}k$ Congruences involving $\binom{4k}{2k}$ and $\binom{3k}k$

2011-08-24

arxiv.org/abs/1108.4840v1

Mathematics

Number Theory

24 pages

Scientific paper

Let $p$ be a prime greater than 3. In the paper we mainly determine
$\sum_{k=0}^{[p/4]}\binom{4k}{2k}(-1)^k$, $\sum_{k=0}^{[p/3]}\binom{3k}k,
\sum_{k=0}^{[p/3]}\binom{3k}k(-1)^k$ and $\sum_{k=0}^{[p/3]}\binom{3k}k(-3)^k$
modulo $p$, where $[x]$ is the greatest integer not exceeding $x$.

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