Question 15
Let $\{a\}$ denote the difference between $a$ and the nearest integer. For example $\{3.8\} = 0.2$, $\{-5.4\} = 0.4$. Show that
$$
\{a\}\{2a\}\{3a\}\ldots\{na\} \geq \frac{\{a\}^n}{2^n}
$$
$$
\{a\}\{2a\}\{3a\}\ldots\{na\} \geq \frac{\{a\}^n}{2^n}
$$