1. Consider the number $N=\sqrt{2009 \cdot 2011 \cdot 2013 \cdot 2015+16}$. Calculate $\left[\frac{N}{2015}\right]$, where $[a]$ represents the integer part of the real number $a$.

Ștefan Ciochină, Brăila
## Solution.

$N=\sqrt{2009 \cdot 2011 \cdot 2013 \cdot 2015+16} \Rightarrow N=\sqrt{(2012-3)(2012-1)(2012+1)(2012+3)+16}$

$\Rightarrow N=2012^{2}-5$

$\left[\frac{N}{2015}\right]=\left[\frac{2012^{2}-5}{2015}\right]=\left[\frac{2015 \cdot 2009+4}{2015}\right]=2009$