欧拉商的同余式及其应用(Ⅲ)

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英文篇名：A Congruence Involving the Quotients of Euler and Its Applications(Ⅲ) 作者：蔡天新 ; 钟豪 ; 陈小航 英文作者：Tian Xin CAI;Hao ZHONG;Shane CHERN;School of Mathematical Sciences, Zhejiang University;Department of Mathematics, Pennsylvania State University,University Park; 关键词：二项式系数 ; Morley同余式 ; 欧拉商 英文关键词：binomial coefficient;;Morley's congruence;;Euler quotient 中文刊名：SXXB 英文刊名：Acta Mathematica Sinica(Chinese Series) 机构：浙江大学数学科学学院;宾夕法尼亚州立大学数学系; 出版日期：2019-07-15 出版单位：数学学报(中文版) 年：2019 期：v.62 基金：国家自然科学基金资助项目(11501052,11571303) 语种：中文; 页：SXXB201904001 页数：12 CN：04 ISSN：11-2038/O1 分类号：3-14

摘要

在2002,2007的文章中,蔡天新等人介绍了一系列关于二项式系数模平方数的同余式.本文将这些同余式进行改进并推广到了模为立方数的情形,得到了许多新的同余式.如对任意正整数k和正奇数n,当e=2,3,4和6时,Π_(d|n)(_(「d/e」)~(kd-1))~(μ(n/d))模n~3的同余式,以及下面这类有趣的同余式■
        In the papers of 2002 and 2007,Cai et al.introduced a series of congruences involving binomial coefficients under perfect moduli.This article generalizes these congruences to cubic cases leading to many new statements.For example,the congruenceΠ_(d|n)(_(「d/e」)~(kd-1))~(μ(n/d))module n~3 for e=2,3,4 and 6,and the following congruence■

引文

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