# N 元二次不定方程式的整數解探討

2008年

## 摘要或動機

+ y² + z² = w²的整數解為(mn、m² + mn、mn + n²、m²+ mn + n² )，這組解被我們發現有多處遺漏，本文以擴展的畢氏定理做基礎修正了他的整數解公式，並推廣取得N

There is a beautiful integer solution formula for the Pythagorean theorem equation,
x² + y² = z² , such as (m² - n² , 2mn ,m² + n² ). The “m＂ and “n＂ of the solution
formula are integer number. A book written by two Chinese mathematicians, Yen Chen-chun
and Sheng Li-jen who expanded the Pythagorean theorem equation to the four variables
squares’ indeterminate equation, x² + y² + z² = w² . They claimed that they found
its integer solution formula, such as (mn , m² + mn , mn + n² , m² + mn + n² ) for
any integer “m＂ and “n＂. But we found it losses many solutions. This paper corrected
their faults due to the expanded Pythagorean theorem built by ourselves. Further
more, we derived a general formula of N variables squares’ indeterminate equation.
Now, we can get integer solutions of the equation, (for all natural number “n＂) easily by choosing integers m1 , m2 , m3 ,……, mn−1 up to you.

「為配合國家發展委員會「推動ODF-CNS15251為政府為文件標準格式實施計畫」，以及 提供使用者有文書軟體選擇的權利，本館檔案下載部分文件將公布ODF開放文件格式， 免費開源軟體可至LibreOffice 下載安裝使用，或依貴慣用的軟體開啟文件。」

N 元二次不定方程式的整數解探討 448 KB 