Question 34
Prove that there are no two distinct positive integers $a$ and $b$, such that $\{\frac{a}{b}\} + \{\frac{b}{a}\} = 0$.
Here $\{x\}$ denotes the difference between $x$ and the greatest integer that does not exceed $x$, for example, $\{\frac{7}{5}\} = \frac{2}{5}$, $\{\frac{2019}{3}\} = 0$ and $\{\frac{2020}{3}\} = \frac{1}{3}$.
Here $\{x\}$ denotes the difference between $x$ and the greatest integer that does not exceed $x$, for example, $\{\frac{7}{5}\} = \frac{2}{5}$, $\{\frac{2019}{3}\} = 0$ and $\{\frac{2020}{3}\} = \frac{1}{3}$.