| 关于伪Smarandache函数的一个问题 |
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| 引用本文： | 杨明顺.关于伪Smarandache函数的一个问题[J].纯粹数学与应用数学,2008,24(3). |
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| 作者姓名： | 杨明顺 |
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| 作者单位： | 渭南师范学院数学系,陕西,渭南,710082 |
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| 摘 要： | 对任意正整n,著名的伪Smarandache函数Z(n)定义为最小的正整数m使得n|m(m 1)/2.本文的主要目的是利用初等方法研究Kenichiro Kashihara提出的"求所有正整数n使得伪smarandache函数Z(n)为n的原根"这一问题,并得到彻底解决.即就是证明了Z(n)为n的原根当且仅当n=2,3,4.
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| 关 键 词： | 伪Smarandache函数 原根 初等方法 |
On a problem of the pseudo Smarandache function |
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| YANG Ming-shun.On a problem of the pseudo Smarandache function[J].Pure and Applied Mathematics,2008,24(3). |
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| Authors: | YANG Ming-shun |
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| Institution: | YANG Ming-shun Department of Mathematics,Weinan Teacher\'s College,Weinan 714000,China |
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| Abstract: | For any positive integer n, the famous pseudo Smarandache function Z(n) is defined as the smallest positive integer m such that n|(m(m+1))/2.The main purpose of this paper is using the elementary method to find all positive integer n such that Z(n) is a primitive root of n. This problem proposed by Kenichiro Kashihara in his book 3], we solved it completely, and proved that Z(n) is a primitive root of n if and only if n = 2, 3, 4. |
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| Keywords: | the pseudo Smarandache function primitive root elementary method |
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