## Subject 2.

Determine the natural values of $n$ for which $(3 x+11, 5 x-3)=2^{n}$, where $x$ is a natural number, and $(a, b)$ represents the greatest common divisor of the numbers $a$ and $b$.
## Subject 2.

If $(3 x+11,5 x-3)=2^{n}$ then $2^{n} / 3 x+11$ and $2^{n} / 5 x-3 \quad$... 2p.

$2^{n} /(3 x+11) \cdot 5-(5 x-3) \cdot 3 \Rightarrow 2^{n} / 64 \quad \ldots 3 \mathbf{p}$.

$\Rightarrow n \in\{0,1,2,3,4,5,6\} \quad$... 2p.