许多组合问题看似与方程无关,若能去伪存真,转换思维角度,转化为不定方程整数解的模型,则往往能化繁为简、柳暗花明.1不定方程整数解的有关结论定理1不定方程x_1+x_2+…+x_k=n(k,n∈N+)的非负整数解的个数为C_(n+k-1)~n.证法1将不定方程x_1+x_2+…+x_k=n的任意一组非负整数解(x_1,x_2,…,x_k)对应于一个由n个圆 Many combinations of problems seem to have nothing to do with the equation, if you can go to the pseudo-true, the conversion of thinking point of view, converted into an indefinite integer integer solution of the model, you can often turn into simple, superficial .1 indefinite equation integer solution of the conclusions Theorem 1 Indefinite equation x_1 + The number of non-negative integer solutions of x_2 + ... + x_k = n (k, n∈N +) is C_ (n + k-1) ~ n. The set of nonnegative integer solutions (x_1, x_2, ..., x_k) corresponds to one consisting of n circles