Problem

Source: Romanian National Olympiad 2024 - Grade 9 - Problem 2

Tags: algebra, fractional part



Let $a$ and $b$ be two numbers in the interval $(0,1)$ such that $a$ is rational and $\{na\} \ge \{nb\},$ for every nonnegative integer $n.$ Prove that $a=b.$ (Note: $\{x\}$ is the fractional part of $x.$)