Lời giải:
\(\left\{\begin{matrix} 5a+3b\vdots 2021\\ 13a+8b\vdots 2021\end{matrix}\right.\Rightarrow 8(5a+3b)-3(13a+8b)\vdots 2021\)
\(\Rightarrow a\vdots 2021\)
\(\left\{\begin{matrix} 5a+3b\vdots 2021\\ a\vdots 2021\end{matrix}\right.\Rightarrow 3b\vdots 2021\Rightarrow b\vdots 2021\)
Ta có đpcm