KöMaL 2026 B5546

For positive integers $a$, $b$, $c$ the values of expressions $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$ and $\frac{a}{c}+\frac{c}{b}+\frac{b}{a}$ are also integers. Prove that $a=b=c$.