Question 35
Do there exist pairwise distinct positive integers $a$, $b$ and $c$, such that $\left\{ \frac{a}{b} + \frac{b}{c} + \frac{c}{a} \right\} = 0$? The fractions are not necessarily irreducible.
Here $\{x\}$ denotes the difference between $x$ and the greatest integer that does not exceed $x$, for example, $\left\{ \frac{7}{5} \right\} = \frac{2}{5}$, $\left\{ \frac{2019}{3} \right\} = 0$ and $\left\{ \frac{2020}{3} \right\} = \frac{1}{3}$.
Here $\{x\}$ denotes the difference between $x$ and the greatest integer that does not exceed $x$, for example, $\left\{ \frac{7}{5} \right\} = \frac{2}{5}$, $\left\{ \frac{2019}{3} \right\} = 0$ and $\left\{ \frac{2020}{3} \right\} = \frac{1}{3}$.