\(\left(2x+3y\right)⋮17\Leftrightarrow13\left(2x+3y\right)⋮17\Leftrightarrow\left(26x+39y\right)⋮17\)
\(\Leftrightarrow\left(26x-17x+39y-34y\right)⋮17\Leftrightarrow\left(9x+5y\right)⋮17\)
Ta có 9x + 5y \(⋮\)17
<=> 17x + 17y - 8x - 12y \(⋮\)17
<=> 17(x + y) - 4(2x + 3y) \(⋮\)17
Vì 17(x + y)\(⋮\)17
<=> 4(2x + 3y) \(⋮\)17
<=> 2x + 3y \(⋮\) 17
=> ĐPCM