论文标题
关于二项式系数和类似猿的数字的超级一致性
Super congruences concerning binomial coefficients and Apéry-like numbers
论文作者
论文摘要
让$ p $是$ p> 3 $的素数，让$ a，b $为两个有理$ p-$整数。在本文中，我们介绍了$ \ sum_ {k = 0}^{p-1} \ binom ak \ binom {-1-a} k \ frac p {k+b} \ pmod {p^2} $。对于$ n = 0,1,2，\ ldots $让$ d_n $和$ b_n $分别为domb和almkvist-zudilin编号。我们还为$$ \ sum_ {n = 0}^{p-1} \ frac {d_n} {16^n}，\ quad \ sum_ {n = 0}^{p-1} \ frac {d_n} {d_n} {4^n} {4^n}，\ quad \ sum_ {n = 0}^{p-1} \ frac {b_n} {（ - 3）^n}，\ quad \ sum_ {n = 0}^{p-1} \ frac {b_n} {b_n} {（ - 27）
Let $p$ be a prime with $p>3$, and let $a,b$ be two rational $p-$integers. In this paper we present general congruences for $\sum_{k=0}^{p-1}\binom ak\binom{-1-a}k\frac p{k+b}\pmod {p^2}$. For $n=0,1,2,\ldots$ let $D_n$ and $b_n$ be Domb and Almkvist-Zudilin numbers, respectively. We also establish congruences for $$\sum_{n=0}^{p-1}\frac{D_n}{16^n},\quad \sum_{n=0}^{p-1}\frac{D_n}{4^n}, \quad \sum_{n=0}^{p-1}\frac{b_n}{(-3)^n},\quad \sum_{n=0}^{p-1}\frac{b_n}{(-27)^n}\pmod {p^2}$$ in terms of certain binary quadratic forms.
