我们常常遇到(或可化为)下列问题:求方程x1+x2+…+xm=n(m,n∈N*,m≤n)的正整数解的个数.下面笔者给出这一问题的计算方法及其应用,供大家参考.一、模型与计数公式上述不定方程正整数解的个数问题可以转化为下列数学模型:把n个相同的小球排成一行,并将它分成m段,每一段至少一个 We often encounter (or can be) the following problem: Find the number of positive integer solutions of the equation x1 + x2 + ... + xm = n (m, n∈N *, m≤n). The following gives the problem The calculation method and its application, for your reference.First, the model and the counting formula The number of positive integer solutions of the above indefinite equation can be converted into the following mathematical model: the n same ball in a row, and it is divided into m Paragraph, at least one in each paragraph