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    Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/7767


    Title: a^n-b^n的原質因子,其中a,b為高斯整數;Primitive Factors of a^n-b^n for a,b Gaussian integers
    Authors: 鄭至人;Zh-Ren Zheng
    Contributors: 數學研究所
    Keywords: 原質因子;高斯整數;分圓多項式;primitive factor;Gaussian integer
    Date: 2001-07-10
    Issue Date: 2009-09-22 11:04:53 (UTC+8)
    Publisher: 國立中央大學圖書館
    Abstract: 這篇論文探討的是a^n-b^n 的原質因子。當a,b 皆為整數時,我們從[1]的介紹中很清楚地看到:除了少數幾個n之外,幾乎所有的a^n-b^n 都有原質因子。本文中,我們將a,b 推廣到高斯整數,但遭遇到困難,因而將a,b 限制成:︱a ︱> = ︱b ︱+1。最後,我們也證明了在此條件之下,除了少數幾個n之外,幾乎所有的a^n-b^n 都有原質因子。 The purpose of this thesis is to study the primitive factors of a^n-b^n, where a,b are nonzero relatively ffgg prime Gaussian integers with |a| > = |b|+1 and n is a positive integer. We have an analogous result to the case where a and b are rational integers: There are only finitely many numbers of n such that a^n-b^n has no primitive factors.
    Appears in Collections:[數學研究所] 博碩士論文

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