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研究生： 沈雅引
論文名稱： 論部分馬可夫數之解
On the Solutions of Certain Markoff Numbers
指導教授： 洪有情
學位類別： 碩士
Master
系所名稱： 數學系
Department of Mathematics
論文出版年： 2007
畢業學年度： 95
語文別： 中文
論文頁數： 20
中文關鍵詞： 馬可夫方程式 、馬可夫數
英文關鍵詞： Markoff equation, Markoff number
論文種類： 學術論文
相關次數： 點閱：147  下載：7 
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    • 這篇論文主要是，藉由探討馬可夫方程式的解（a,b,c)與斐波那契（Fibnacci）數列、佩爾（pell）數列間特殊的關係，加以證明：當c是5乘以一個質數的n次方的形式時，其中這個質數被4除餘1，若a<13，此方程式只有（2，169，985）唯一一組解。

    In this dissertation, by virtue of the relation between the solutions (a, b, c) of the Markoff equation and Fibonacci numbers, Pell numbers, we show that if c = 5p^n where p is a prime congruent to 1 modulo 4, and a < 13 then
    (2, 169, 985) is the unique solution of Markoff equation.

    1. Introduction 1 2. Preliminary 4 3. The first case : a = 1 9 4. The second case : a = 2 14 References 19

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