Question 126
Let $a$ and $b$ be two real numbers in the interval $(0, 1)$, so that $a$ is a rational number and
$$
\{na\} \ge \{nb\}, \text{ for every natural number } n.
$$
Prove that $a = b$. (We denote by $\{x\}$ the fractional part of the real number $x$.)
$$
\{na\} \ge \{nb\}, \text{ for every natural number } n.
$$
Prove that $a = b$. (We denote by $\{x\}$ the fractional part of the real number $x$.)