Problem 1. Calculate: $\left(37^{2016}: 1369^{1008}\right):\left(2^{2016}-2^{2015}-\ldots-2^{2}-2-1\right)$
## Solution and Scoring

![](https://cdn.mathpix.com/cropped/2024_06_07_ed9ce7b72d1b7a3ea09ag-2.jpg?height=58&width=1218&top_left_y=846&top_left_x=252)

Perform the calculation: $\left(37^{2016}:\left(37^{2}\right)^{1008}\right):\left(2^{2016}-2^{2015}-\ldots-2^{2}-2-1\right)=\ldots \ldots .1 p$

$$
\begin{aligned}
& \left(37^{2016}: 37^{2016}\right):\left(\left(2 \cdot 2^{2015}-2^{2015}\right)-\ldots-2^{2}-2-1\right)=\ldots \ldots .2 p \\
& 1:\left(2^{2015}-\ldots-2^{2}-2-1\right)=\ldots 1:(2-1)=1: 1=1 \ldots \ldots \ldots \ldots .3 p
\end{aligned}
$$