Cho a, b ∈ N . Chứng tỏ rằng nếu 5a+3b và 13a+8b cùng chia hết cho 2018 thì a, b cũng chia hết cho 2018 .

$\text{(*)}$

$5a+3b$ $\vdots$ $2018$ 

$65a+39b$ $\vdots$ $2018$

$\text{(**)}$

$13a+8b$ $\vdots$ $2018$

$65a+40b$ $\vdots$ $2018$

$\text{Từ (*)(**)}$

$\text{=>} $b$ $\vdots$ $2018$

$\text{->}$ $3b$ $\vdots$ $2018$

$\text{->}$ $5b$ $\vdots$ $2018$

$ƯCLN(5,2018)=1$

$\text{=>}$ $a$ $\vdots$ $2018$