## Problem 1

Find the natural numbers that satisfy the relation:

$9 \leq \sqrt{\sqrt{2 n+2013}+\sqrt{2 n+2009}}+\sqrt{\sqrt{2 n+2013}-\sqrt{2 n+2009}}<10$.
## Problem 1

$81 \leq 2 \sqrt{2 n+2013}+4<100 \quad$ (3p). $\quad 77^{2} \leq 4(2 n+2013)<96^{2} \quad$ (1p) $-2123 \leq 8 n<1164 \quad$ (2p). Therefore $n \in\{0,1, \ldots, 145\} \quad$ (1p).