Congruences involving $\binom{2k}k^2\binom{4k}{2k}m^{-k}$

Details Congruences involving $\binom{2k}k^2\binom{4k}{2k}m^{-k}$ Congruences involving $\binom{2k}k^2\binom{4k}{2k}m^{-k}$

2011-04-15

arxiv.org/abs/1104.3047v2

Mathematics

Number Theory

14 pages

Scientific paper

Let $p>3$ be a prime, and let $m$ be an integer with $p\nmid m$. In the
paper, by using the work of Ishii and Deuring's theorem for elliptic curves
with complex multiplication we solve some conjectures of Zhi-Wei Sun concerning
$\sum_{k=0}^{p-1}\binom{2k}k^2\binom{4k}{2k}m^{-k}\mod {p^2}$.

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