Question 118
Let $n \geqslant 1$ an integer. It is assumed that there are exactly 2005 pairs $(x, y)$ of natural integers such as $\frac{1}{x}+\frac{1}{y}=\frac{1}{n}$. Show that $n$ is the square of an integer. N.B. If $x \neq y$ then $(x, y) \neq (y, x)$.