3. Determine the natural numbers that can replace the unknowns $a, b$ and $c$ in the equation:

$$
\frac{283}{255}=1+\frac{1}{a+\frac{1}{b+\frac{1}{c}}}
$$
First method:

$$
\begin{aligned}
\frac{283}{255} & =1+\frac{28}{255} \\
& =1+\frac{1}{\frac{255}{28}} \\
& =1+\frac{1}{9+\frac{3}{28}} \\
& =1+\frac{1}{9+\frac{1}{\frac{28}{3}}} \\
& =1+\frac{1}{9+\frac{1}{9+\frac{1}{3}}}
\end{aligned}
$$

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