| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 洪雅婷 | zh_TW |
| DC.creator | Ya-Ting Hung | en_US |
| dc.date.accessioned | 2006-6-21T07:39:07Z | |
| dc.date.available | 2006-6-21T07:39:07Z | |
| dc.date.issued | 2006 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=93221014 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.abstract | 我們考慮特別的整係數方程式去尋找整數解或有理數解。Ratat和Goormaghtigh觀察出當x,y,m,n為正整數時，(x,y,m,n)=(5,2,3,5)和(90,2,3,13)是方程式 (x^m-1)/(x-1)=(y^n-1)/(y-1) 的解。因此，猜想此方程式只有這兩組解。現在，我們集中焦點在m=3。此時方程式有兩組已知的解。除了那兩組解之外的解就稱為例外解。這篇論文，主要是考慮當n=4時，此方程式沒有例外解。 | zh_TW |
| dc.description.abstract | We consider special Diophantine equations with integral coefficient and seek
integral or rational solutions. Ratat[1] and Goormaghtigh [2] observed that
31=(2^5-1)/(2-1)=(5^3-1)/(5-1)
and 8191=(2^13-1)/(2-1)=(90^3-1)/(90-1)
are solutions of the Diophantine equation
(x^m-1)/(x-1)=(y^n-1)/(y-1)
; x > 1; y > 1; n > m > 2.....(1)
Now, we will focus our attention on the equation
(x^3-1)/(x-1)=(y^n-1)/(y-1)
; n > 2; x > 1; y > 1 with x > y.....(2)
Equation (2) has two known solutions (x, y, n) = (5, 2, 5), (90, 2, 13). Any other
solution (x, y, n) of (2) will be called exceptional. In this paper, we show that this
equation (2) has no exceptional solution when n = 4. | en_US |
| DC.subject | Diophantine Equation | en_US |
| DC.title | On the Diophantine Equation of (x^m-1)/(x-1)=(y^n-1)/(y-1) | en_US |
| dc.language.iso | en_US | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |