| 二元一次不定方程的变量替换求解方法及其计算复杂度分析 |
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| 引用本文： | 陈功. 二元一次不定方程的变量替换求解方法及其计算复杂度分析[J]. 盐城工学院学报(自然科学版), 2017, 30(4): 68-71 |
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| 作者姓名： | 陈功 |
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| 作者单位： | 上海交通大学 电子信息与电气工程学院, 上海 200240 |
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| 基金项目： | 国家科技重大专项课题(2013ZX03002004) |
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| 摘 要： | 对运用变量替换法求解二元一次不定方程的过程作一般化处理,得到其通解公式和特解计算公式,并证明了所得结果与运用辗转相除法所得的经典结论相一致;进一步通过计算复杂度的估计,得出两种解法计算量相当的结论。
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| 关 键 词： | 二元一次不定方程；变量替换；辗转相除；通解；计算复杂性；位运算 |
| 收稿时间： | 2017-05-23 |
Solution of Variable Substitution for Linear Indeterminate Equation in Two Unknowns and Analysis of Its Computation Complexity |
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| CHEN Gong. Solution of Variable Substitution for Linear Indeterminate Equation in Two Unknowns and Analysis of Its Computation Complexity[J]. Journal of Yancheng Institute of Technology(Natural Science Edition), 2017, 30(4): 68-71 |
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| Authors: | CHEN Gong |
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| Affiliation: | School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai200240, China |
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| Abstract: | This paper deals with the process of solving the linear indeterminate equation in two unknowns with variable substitution method, and obtains the general solution formula and the special solution formula. It is proved that the results are consistent with the classical conclusions obtained by using the method of successive division. The computational complexity is further estimated, and the conclusion is drawn that the two methods have the same calculation amount. |
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| Keywords: | linear indeterminate equation in two unknowns variable substitution division algorithm general solution computational complexity bit operation |
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