Example 1.5.3.

How many integer solutions are there to the equation

\begin{equation*} x_1 + x_2 + x_3 + x_4 + x_5 = 13\text{.} \end{equation*}

(An integer solution to an equation is a solution in which the unknown must have an integer value.)

  1. where \(x_i \ge 0\) for each \(x_i\text{?}\)

  2. where \(x_i > 0\) for each \(x_i\text{?}\)

  3. where \(x_i \ge 2\) for each \(x_i\text{?}\)

Solution.
in-context