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《数学通报》1980年第4期中有一篇文章《求方程Ax+By=Cxy的正整数解》,该文的解法主要是依据整数大小的性质。大小的性质并非整数所特有。因此该文一般解法稍嫌烦琐。解不定方程的常规解法是依据整数的整除性质,这是整数所特有的性质。抓住特点的解法,一般要简明些。下面用整除的性质给出一个解法,由该法容易求全部整数解,不限于正整数解。
In the 4th issue of Mathematical Bulletin 1980, there was an article “Find the Positive Integer Solution to the Equation Ax+By=Cxy”. The solution of this paper is mainly based on the property of integer size. The nature of size is not unique to integers. Therefore, the general solution of this article is a bit cumbersome. The conventional solution to solving indefinite equations is based on the integer divisibility of integers, which is an integer-specific property. Seize the characteristics of the solution, generally concise. In the following, a solution is given by the property of integer divisibility. This method is easy to find all integer solutions, not limited to positive integer solutions.