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

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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:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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