Question

Chứng minh rằng: Nếu 5x-12y chia hết cho 17 thì 18x+y chia hết cho 17

Answer 1

có: với x,y là số nguyên

\(\left(5x-12y\right)⋮17\Rightarrow\left[\left(5x-12y\right)+17y\right]⋮17\Rightarrow5.\left(x+y\right)⋮17\)

mà \(\left(5;17\right)=1\Rightarrow x+y⋮17\)

\(\Rightarrow\left(x+y+17x\right)⋮17\Rightarrow\left(18x+y\right)⋮17\left(đpcm\right)\)

Answer 2

$\left(5x-12y\right)⋮17\Rightarrow \left[\left(5x-12y\right)+17y\right]⋮17\Rightarrow 5.\left(x+y\right)⋮17$

mà $\left(5;17\right)=1\Rightarrow x+y⋮17$

$\Rightarrow \left(x+y+17x\right)⋮17\Rightarrow \left(18x+y\right)⋮17\left(đpcm\right)$