Đáp án đúng:
Giải chi tiết:Ta có :
\(\begin{array}{l}(5a + 3b) \vdots 2018 \Rightarrow 8.(5a + 3b) \vdots 2018\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\\\left( {13a + 8b} \right) \vdots 2018 \Rightarrow 3.\left( {13a + 8b} \right) \vdots 2018\,\,\,\,\,\,\,\,\,\,\left( 2 \right)\\ \Rightarrow 8.(5a + 3b) - 3.\left( {13a + 8b} \right)\,\,\,\,\,\,\,\,\, \vdots 2018\\ \Rightarrow \,\,\,\,\,\,40a + 24b - 39a - 24b\,\,\,\,\,\,\,\,\,\, \vdots 2018\\ \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \vdots 2018\end{array}\)
Mà \(5a + 3b \vdots 2018 \Rightarrow \,\,\,\,\,\,3b \vdots 2018\) (trong đó \(\left( {3;\,2018} \right) = 1\))
\( \Rightarrow b \vdots 2018\)
Vậy \(5a + 3b\) và \(13a + 8b\) cùng chia hết cho 2018 thì a và b cũng chia hết cho 2018.
