MathNet 2025 — 50 problems — Part 01 Question 26

Consider positive real numbers $m, n, a, b, c$, such that $m \gt n$ and $|ma - nb| \le c(m - n)$, $|mb - nc| \le a(m - n)$, $|mc - na| \le b(m - n)$. Prove that $a = b = c$.

Lucian Petrescu