论文标题
通过好奇的身份证明了某些猜想的超几何超级优势
Proof of some conjectural hypergeometric supercongruences via curious identities
论文作者
论文摘要
在本文中，我们证明了Z.-W。猜想的几个超级企业。十年前的太阳通过某些奇怪的高几幅身份。例如，对于任何prime $ p> 3 $，我们表明$$ \ sum_ {k = 0}^{p-1} \ frac {\ binom {\ binom {4K} {2K+1} \ binom {2k} k} k} k} \ sum_ {k = 0}^{p-1} \ frac {\ binom {2k} {k} {k} \ binom {3K} {k}} {24^k} \ equiv \ equiv \ equiv \ okent {cases} case} \ binom {case} ＆\ mbox {if} \ p \ equiv1 \ pmod {3}，\\ p/\ binom {（2p+2）/3} {（p+1）/3} \ pmod {p^2} {p^2} \＆\ mbox {if} \ p \ p \ p \ equiv2 $ equ}这样的类型。
In this paper, we prove several supercongruences conjectured by Z.-W. Sun ten years ago via certain strange hypergeometric identities. For example, for any prime $p>3$, we show that $$\sum_{k=0}^{p-1}\frac{\binom{4k}{2k+1}\binom{2k}k}{48^k}\equiv0\pmod{p^2},$$ and $$ \sum_{k=0}^{p-1}\frac{\binom{2k}{k}\binom{3k}{k}}{24^k}\equiv\begin{cases}\binom{(2p-2)/3}{(p-1)/3}\pmod{p^2}\ &\mbox{if}\ p\equiv1\pmod{3},\\ p/\binom{(2p+2)/3}{(p+1)/3}\pmod{p^2}\ &\mbox{if}\ p\equiv2\pmod{3}.\end{cases} $$ We also obtain some other results of such types.
