Question 87
Let $a$ be a natural odd number which is not a perfect square. If $m$ and $n$ are strictly positive integers, prove that
$$
\begin{aligned}
\text{a)} \quad & \{m(a + \sqrt{a})\} \neq \{n(a - \sqrt{a})\}, \\
\text{b)} \quad & [m(a + \sqrt{a})] \neq [n(a - \sqrt{a})].
\end{aligned}
$$
$$
\begin{aligned}
\text{a)} \quad & \{m(a + \sqrt{a})\} \neq \{n(a - \sqrt{a})\}, \\
\text{b)} \quad & [m(a + \sqrt{a})] \neq [n(a - \sqrt{a})].
\end{aligned}
$$