Question

Rezolvati in multimea numerelor intregi ecuatia :xy-3x+2y=1

Answer 1

$\it\ \ \ x,\ y\in\mathbb{Z}\\ \\ xy-3x+2y=1|_{-6} \Rightarrow (xy+2y)-3x-6=-5 \Rightarrow y(x+2)-3(x+2)=-5 \Rightarrow \\ \\ \Rightarrow (x+2)(y-3)=-5=-1\cdot5=5\cdot(-1)\ \ \ \ \ \ (*)\\ \\ (*) \Rightarrow \begin{cases}\it x+2=-1 \Rightarrow x=-3;\ \ \ y-3=5 \Rightarrow y=8\\ \\ \it x+2=5 \Rightarrow x=3;\ \ y-3=-1 \Rightarrow y=2 \end{cases}$

$\it (x,\ y)\in\{(-3,\ 8),\ \ (3,\ 2)\}$