| 关于丢番图方程x2+by2＝z2n及x2+by2＝bz2n的整数解 |
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| 引用本文： | 张文忠.关于丢番图方程x2+by2＝z2n及x2+by2＝bz2n的整数解[J].西华大学学报(自然科学版),2005,24(5):75-77. |
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| 作者姓名： | 张文忠 |
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| 作者单位： | 西华大学数学与计算机学院,四川,成都,610039 |
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| 摘 要： | 本文作者证明了丢番图方程x^2＋by^2=z^2^n及x^2＋by^2=bz^2^n都有无穷多组整数解，同时给出了逐步递推求出其全部整数解的方法。
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| 关 键 词： | 丢番图方程 非平凡解 整数解 最大公因数 数学归纳法 |
| 文章编号： | 1673-159X(2005)05-0075-03 |
| 收稿时间： | 2005-05-19 |
| 修稿时间： | 2005年5月19日 |
On The Solution to Integer of Diophantine Equation x2+by2=z2n and x2+by2=bz2n |
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| ZHANG Wen-zhong.On The Solution to Integer of Diophantine Equation x2+by2=z2n and x2+by2=bz2n[J].Journal of Xihua University:Natural Science Edition,2005,24(5):75-77. |
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| Authors: | ZHANG Wen-zhong |
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| Affiliation: | School of Computers and Mathematical-Physical Science, Xihna University,Chengdu 610039 China |
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| Abstract: | This article proves that there are infinite integer solutions to Diophantine equation x~2+by~2=z~(2~n) and x~2+by~2=bz~(2~n),at the same time presents the method to find all integer solutions to them by using step-recursion approach. |
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| Keywords: | diophantine equation non-trivial solution integer solution greatest common measure mathematical induction |
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