# Beggar's Method

### Problem

Find the number of integer solutions i.e. ordered pairs $\left(x_1, x_2, \ldots , x_r \right)$ such that

$x_1 + x_2 + \ldots + x_r = n, \quad x_i \geq 0, x_i \in \mathbb{Z}$

### Solution

The number of such solutions is given by