Question 110
The mediant of two rational numbers $u$ and $v$ is $x = \frac{a+c}{b+d}$, where $\frac{a}{b}$ and $\frac{c}{d}$ are the reduced fractions of $u$ and $v$ respectively. Prove that for any two distinct positive rational numbers $u$ and $x$, there exist infinitely many positive rational numbers $v$, such that $x$ is the mediant of $u$ and $v$.