| 一个包含Smarandache LCM函数的方程 |
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| 引用本文： | 贺艳峰,潘晓玮. 一个包含Smarandache LCM函数的方程[J]. 数学学报, 2008, 51(4): 779-786. DOI: CNKI:SUN:SXXB.0.2008-04-020 |
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| 作者姓名： | 贺艳峰 潘晓玮 |
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| 作者单位： | 西北大学数学系,西北大学数学系 西安 710069 延安大学计算机学院 延安 716000,西安 710069 西安医学院 西安 710021 |
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| 摘 要： | 对任意正整数n,著名的Smarandache LCM函数SL(n)定义为最小的正整数k,使得n|[1,2,…,k],其中[1,2,…,k]表示1,2,…,k的最小公倍数.本文利用初等方法研究一类包含Smarandache LCM函数方程的可解性,并获得了给定方程的所有正整数解.
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| 关 键 词： | Smarandache LCM函数 方程 正整数解 |
| 收稿时间： | 2007-04-05 |
An Equation Involving the Smarandache LCM Function |
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| Affiliation: | Yan Feng HE Department of Mathematics,Northwest University,Xi'an 710069,P.R.China College of Mathematics and Computer Science,Yan'an University,Yan'an 71600,P.R.China Xiao Wei PAN Department of Mathematics,Northwest University,Xi'an 710069,P.R.China Xi'an Medical University,Xi'an 710021,P.R.China |
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| Abstract: | For any positive integer n,the famous Smarandache LCM function SL(n) is defined as the smallest positive integer k such that n|[1,2,…,k],where [1,2,…,k] denotes the least common multiple of 1,2,…,k.The main purpose of this paper is to use the elementary methods to study the solutions of an equation involving the Smarandache LCM function SL(n),and obtain all positive solutions of this equation. |
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| Keywords: | Smarandache LCM function equation positive integer solutions |
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