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PDF(443 KB)
PDF(443 KB)
欧拉商的同余式及其应用(III)
A Congruence Involving the Quotients of Euler and Its Applications (Ⅲ)
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，Πd|n（└d/e┘kd-1）μ(n/d)模n3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 congruence Πd|n（└d/e┘kd-1）μ(n/d) module n3 for e=2, 3, 4 and 6, and the following congruence
二项式系数 / Morley同余式 / 欧拉商 {{custom_keyword}} /
binomial coefficient / Morley's congruence / Euler quotient {{custom_keyword}} /
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国家自然科学基金资助项目（11501052，11571303）
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