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Proof of a conjectural supercongruence modulo $p^5$ (2109.09877v1)

Published 20 Sep 2021 in math.NT

Abstract: In this paper we prove the supercongruence $$\sum_{n=0}{(p-1)/2}\frac{6n+1}{256n}\binom{2n}n3\equiv p(-1){(p-1)/2}+(-1){(p-1)/2}\frac{7}{24}p4B_{p-3}\pmod{p5}$$ for any prime $p>3$, which was conjectured by Sun in 2019.

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