Victor J W Guo
Articles written in Proceedings – Mathematical Sciences
Volume 130 All articles Published: 20 October 2020 Article ID 0063 Article
Proof of a supercongruence conjectured by Sun through a q-microscope
In 2011, Sun (
$$\frac{1}{m^2\left({m-1}\atop{(m-1)/2}\right)}\left(\sum^{(mp-1)/2}_{k=0}\frac{{\left(2k\atop k\right) k}}{8^k}-\left(\frac{2}{p}\right)\sum^{(m-1)/2}_{k=0}\frac{\left({2k}\atop{k}\right)}{8^k}\right)\equiv 0 ({\rm mod}\, p^2).$$
By applying the creative microscoping method introduced by Guo and Zudilin (
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