| 同余方程(组)的整数处理方法 |
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| 引用本文： | 刘英,王路群,李凤霞,刘冬丽.同余方程(组)的整数处理方法[J].哈尔滨师范大学自然科学学报,2011,27(3):12-15. |
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| 作者姓名： | 刘英 王路群 李凤霞 刘冬丽 |
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| 作者单位： | 黑龙江外国语学院 |
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| 基金项目： | 黑龙江省高等学校教改工程项目(一般项目序号96) |
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| 摘 要： | 将同余方程组n∑j=1aijxj ≡bi(modmi)(i=1,…,k)化为整系数方程组n∑j=1aijxj-mxn+i=bi(i=1,…,k),利用文献2]中提供的通过对整数矩阵的初等变换方法处理解的存在性与具体求解.另外,对同余方程组x≡ai(modmi),1≤i≤k,在有解时提出求解公式x≡M1/db1a1+…...
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| 关 键 词： | 同余方程(组) 整系数线性方程组 整数矩阵 初等变换 不变因数 |
Using Integer to Solve the System of Congruences |
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| Liu Ying
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Wang Luqun
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Li Fengxia
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Liu Dongli.Using Integer to Solve the System of Congruences[J].Natural Science Journal of Harbin Normal University,2011,27(3):12-15. |
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| Authors: | Liu Ying Wang Luqun Li Fengxia Liu Dongli |
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| Institution: | (Heilongjiang International University) |
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| Abstract: | Transform the system of congruences n∑j=1aijxj ≡bi(modmi)(i=1,…,k) into the system of integeral coefficient linear equations n∑j=1aijxj-mxixn+i=bi(i=1,…,k),using elementary transformation of integer matrix in 2] to study the existence of solution and how to solve it.Otherwise for the system of congruences x≡ ai(modmi),1≤i≤k,when it has solution and its formula is x≡(M1/d)b1a1+…+(Mk/d)bkak(mod m1,…,mk]) ,using elementary transformation of 3] to compute bi(1≤i≤k) and get the solution of the system of congruences. |
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| Keywords: | The system of congruences The system of integeral coefficient linear equations Integer matrix Elementary transformation Invariant factors |
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