一类多元一次不定方程的正整数解的组数问题

不定方程，是指未知数的个数多于独立方程的个数的方程或方程组．一般地，不定方程存在无穷多组解．因此，要求一个不定方程的全部的解，是相当困难的，有时甚至是不可能的或不现实的．通过利用容斥原理和排列组合的有关知识求得一类不定方程的正整数解的组数并得到一些解该类型题的常用的技巧与方法．

On the Class Number of Positive Integer Solution of Multi-head Linear Diophantine Equation

Diophantine equation is the equation or equation class whose unknown numbers are more than that of independent equation. Generally, diophantine equation has unlimited solution, so it is difficult to obtain all the solutions of a diophantine equation, or impossible or unrealistic. In the paper, the author has made use of inclusion-exclusion principle and permutation and combination to obtain the class number of positive integer solution of multi-head linear diophantine equation and some common techniques and methods to this kind of problems.