| 关于二元线性方程的正整数解的个数 |
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| 引用本文： | 郑英伟.关于二元线性方程的正整数解的个数[J].西南师范大学学报(自然科学版),1999,24(4):410-412. |
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| 作者姓名： | 郑英伟 |
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| 作者单位： | 湛江市电视大学数理教研室,湛江,524003 |
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| 摘 要： | 设a，b，c，k是适合gcd（a，b）=1的正整数．证明了：恰有ab个不同的正整数c可使方程ax by=c共有k组正整数解（x，y），而且c的最大值和最小值分别是ab（k＋1）和ab（k-1）＋a＋b．
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| 关 键 词： | 二元线性方程 正整数解 解数 |
On the Number of Positive Integer SOlutions of Binary Linear Equations |
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| Zheng Yingwei.On the Number of Positive Integer SOlutions of Binary Linear Equations[J].Journal of Southwest China Normal University(Natural Science),1999,24(4):410-412. |
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| Authors: | Zheng Yingwei |
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| Abstract: | Let a, b, c, k be positive integers with ged (a, b) = 1. It is proved that there exist exactly abdistinct c which make the equation ax by = c to have k positive integer solutions (x, y), Moreover,the maximum and the mnimum of c are ab(k 1) and ab(k - 1) a b respectively. |
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| Keywords: | binary linear equations postive integer solutions number of solutions |
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