$3x + 5y - xy = 17$
$⇒ 3x + y(5 - x) = 17$
$⇒ -3(5 - x)+ y(5-x) = 17 + (-15) = 2$
$⇒ (5-x)(-3 +y) = 2$
`⇒ (5 - x) ; (y - 3) \in Ư(2)={±1 ; ±2}`
Ta có bảng sau :
$\begin{array}{|c|c|} \hline 5- x&1&-1&2&-2 \\\hline y - 3&2&-2&1&-1 \\\hline x&4&6&3&7 \\\hline y - 3&5&1&4&2 \\\hline \end{array}$
Vậy $(x ; y) = (4 ; 5) ; (6 ; 1) ; (3 ; 4 ) ; (7 ; 2)$