Question 9
Let $N$ denote the number of ordered 9-tuples $(x_1, x_2, \dots, x_9)$ of positive integers such that
$$
\frac{1}{x_1} + \frac{1}{x_2} + \dots + \frac{1}{x_9} = 1.
$$
Decide if $N$ is even or odd. Justify your answer.
$$
\frac{1}{x_1} + \frac{1}{x_2} + \dots + \frac{1}{x_9} = 1.
$$
Decide if $N$ is even or odd. Justify your answer.