论文标题
有关广义中央三项系数的一致性
Congruences concerning generalized central trinomial coefficients
论文作者
论文摘要
对于任何$ n \ in \ Mathbb {n} = \ {0,1,2，\ ldots \} $和$ b，c \ in \ Mathbb {z} $，概括的中央trinomial系数$ t_n（b，c）$表示$ x^n $ in the Eppent of Expention of Expention of x^n $ clespention oppenting oppents令$ p $是一个奇怪的素数。在本文中，我们确定$ \ sum_ {k = 0}^{p-1} t_k（b，c）^2/m^k $ modulo $ p^2 $ for Integers $ m $具有某些限制。作为应用，我们确认了太阳的一些猜想[Sci。中国数学。 57（2014），1375--1400]。
For any $n\in\mathbb{N}=\{0,1,2,\ldots\}$ and $b,c\in\mathbb{Z}$, the generalized central trinomial coefficient $T_n(b,c)$ denotes the coefficient of $x^n$ in the expansion of $(x^2+bx+c)^n$. Let $p$ be an odd prime. In this paper, we determine the summation $\sum_{k=0}^{p-1}T_k(b,c)^2/m^k$ modulo $p^2$ for integers $m$ with certain restrictions. As applications, we confirm some conjectural congruences of Sun [Sci. China Math. 57 (2014), 1375--1400].
