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Number of solutions to linear equation $x_1+x_2+\dots+x_n=m$ when the domain of $x_i\ne$ domain of $x_j$
In the lecture notes of one of my previous classes, it was used that if we have an equation of the form
$$\tag{1}
x_1+x_2+\dots+x_n=m
$$
then the total number of solutions, when each $x_i$ is a non-...
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