| 不定方程x(x+1)(x+2)(x+3)=11y(y+1)(y+2)(y+3) |
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| 引用本文： | 程瑶,马玉林.不定方程x(x+1)(x+2)(x+3)=11y(y+1)(y+2)(y+3)[J].重庆师范大学学报(自然科学版),2007,24(3):27-30. |
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| 作者姓名： | 程瑶 马玉林 |
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| 作者单位： | 重庆师范大学,数学与计算机科学学院,重庆,400047 |
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| 基金项目： | 重庆市教委科研基金项目(No.010204) |
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| 摘 要： | 运用了一种初等的证明方法,对一个不定方程x(x 1)(x 2)(x 3)=11y(y 1)(y 2)(y 3)的正整数解进行了研究。证明过程中仅涉及到了初等的数论知识,就是采用了递归序列的方法,证明了不定方程x(x 1)(x 2)(x 3)=11y(y 1)(y 2)(y 3)无正整数解,同时这个证明过程也给出了这个不定方程组的全部整数解,它们是(x,y)=(-3,0),(-3,-1),(-3,-2),(-3,-3),(-2,0),(-2,-1),(-2,-2),(-2,-3),(-1,0),(-1,-1),(-1,-2),(-1,-3),(0,0),(0,-1),(0,-2),(0,-3)。
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| 关 键 词： | 不定方程 整数解 递归序列 |
| 文章编号： | 1672-6693（2007）03-0027-04 |
| 收稿时间： | 2006-09-06 |
| 修稿时间： | 2006-09-062007-05-08 |
The Diophantine Equation x(x+1)(x+2)(x+3)=11y(y+1)(y+2)(y+3) |
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| CHENG Yao,MA Yu-lin.The Diophantine Equation x(x+1)(x+2)(x+3)=11y(y+1)(y+2)(y+3)[J].Journal of Chongqing Normal University:Natural Science Edition,2007,24(3):27-30. |
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| Authors: | CHENG Yao MA Yu-lin |
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| Institution: | College Of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China |
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| Abstract: | In this paper using the method of recurrence sequences we show that there does not exist positive solution in the equation of the title.In fact,we obtain a more general result that the only integer solutions of the Diophantine equation is as follows: x(x 1)(x 2)(x 3)=11y(y 1)(y 2)(y 3)are(x,y)=(-3,0),(-3,-1),(-3,-2),(-3,-3),(-2,0),(-2,-1),(-2,-2),(-2,-3),(-1,0),(-1,-1),(-1,-2),(-1,-3),(0,0),(0,-1),(0,-2),(0,-3). |
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| Keywords: | Diophantine equation positive integer solution recurrence sequence |
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