RO-NMO 2014 Problem 92

Let $a$ be an odd natural that is not a perfect square, and $m,n\in\mathbb{N} .$ Then

a) $\left\{ m\left( a+\sqrt a \right) \right\}\neq\left\{ n\left( a-\sqrt a \right) \right\}$ b) $\left[ m\left( a+\sqrt a \right) \right]\neq\left[ n\left( a-\sqrt a \right) \right]$

Here, $\{\},[]$ denotes the fractionary, respectively the integer part.