期刊论文

关于二项式系数的若干新同余式

中文

数学进展

1000-0917

2018

47

4

525-542

10.11845/sxjz.2017004b

The first and third authors are supported by NSFC （No. 11571303）. The second author is supported by NSFC （No. 11501052）.

本校为其他机构

令$k$为正整数,$p$为素数.设$1 \le a \le p - 1$,$1 \le b \le \frac{{p - 1}}{2}$,本文研究了二项式系数$\left( {\begin{array}{*{20}{c}}{\left( {k + 1} \right)p - a}\\{p - a}\end{array}} \right)$,$\left( {\begin{array}{*{20}{c}}{kp - 1}\\{p - a}\end{array}} \right)$和$\left( {\begin{array}{*{20}{c}}{kp + \frac{{p - 1}}{2} \pm b}\\{\frac{{p - 1}}{2} \pm b}\end{array}} \right)$,$\left( {\begin{array}{*{20}{c}}{kp - 1}\\{\frac{{p - 1}}{2} \pm b}\end{array}} \right)$的同余性质.并得到了一个Morley同余式的推广,以及$\left( {\begin{array}{*{20}{c}}{\left( {k ...

Let $k$ be a positive integer and $p$ be a prime. We give some congruences involving the binomial coefficients $\left( {\begin{array}{*{20}{c}}{\left( {k + 1} \right)p - a}\\{p - a}\end{array}} \right)$,$\left( {\begin{array}{*{20}{c}}{kp - 1}\\{p - a}\end{array}} \right)$ with $1 \le a \le p - 1$ and $\left( {\begin{array}{*{20}{c}}{kp + \frac{{p - 1}}{2} \pm b}\\{\frac{{p - 1}}{2} \pm b}\end{array}} \right)$,$\left( {\begin{array}{*{20}{c}}{kp - 1}\\{\frac{{p - 1}}{2} \pm b}\end{array}} \right)$ with $1 \le b \le \frac{{p - 1}}{2}$ In particular, we get a generalization of Morley's congruenc...