论文标题
涉及两个二项式系数的产品模型$ p^4 $
Supercongruences involving products of two binomial coefficients modulo $p^4$
论文作者
论文摘要
在本文中，我们主要证明了Z.-W的一致性猜想。 sun \ cite {sjnt}：让$ p> 5 $为素数。然后$ \ sum_ {k =（p+1）/2}^{p-1} \ frac {\ binom {\ binom {2k} k^2} {k16^k} \ equiv- \ equiv- \ equiv- \ frac {21} 2H_ {p-1} \ pmod {p pmod {p pmod {p^hormod {p^hormonem $ n $ n $ n $
In this paper, we mainly prove a congruence conjecture of Z.-W. Sun \cite{Sjnt}: Let $p>5$ be a prime. Then $$ \sum_{k=(p+1)/2}^{p-1}\frac{\binom{2k}k^2}{k16^k}\equiv-\frac{21}2H_{p-1}\pmod{p^4}, $$ where $H_n$ denotes the $n$-th harmonic number.
