以下为句子列表：
英文: An elementary proof of the Diophantine equation (The equation abbreviated) is given by using recursion sequence method.
中文: 摘要运用递推序列法，给出组合数丢番图方程(方程式略)的一个初等解法。
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英文: By elementary rank transformations of matrix, a method has been obtained to solve linear diophantine equation with some variables. The method overcomes the deficiency of traditional method.
中文: 摘要利用矩阵的初等列变换，给出了求解多元线性不定方程的一种方法，该方法改进了传统方法计算量大、步骤多的缺点。
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