Monday, 30 June 2014

number theory - In how many solutions of equation : $x_1+x_2+...+x_n=m$

In how many solutions of equation: $x_1+x_2+...+x_n=m$ satisfied: $x_i\in \mathbb{N}(i=\overline{1,n}),1\le x_i\le 26,n\le m\le 26n,m\in \mathbb{N}$




This is my try:
Let $t_i=x_i-1\implies \sum\limits_{i=1}^{n}t_i=\sum\limits_{i=1}^{n}x_i-n=m-n$, where $0\le t_i\le 25$.
And I don't know how to solve it when $0\le t_i\le 25$.


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