MathNet 2003 — Part 02 Question 82

Let $a$, $b$, $c$ be lengths of triangle sides, $p = \frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ and $q = \frac{a}{c} + \frac{c}{b} + \frac{b}{a}$. Prove that $|p - q| \lt 1$.