Răspuns:
[tex] (x, y)\in\left\{(0,-4),(2,2),(-2,3),(4,0)\right\} [/tex]
Explicație pas cu pas:
[tex]\dfrac{x-1}{3}=\dfrac{1}{y+1}\iff (x-1)(y+1)=3.[/tex]
Fiind 3 un număr ireductibil, avem că
[tex](x-1)\mid 3 \implies x-1\in\left\{-1,1,-3,3\right\}[/tex] adică [tex]x\in\left\{0,2,-2,4\right\}.[/tex]
[tex] x=0 \implies -(y+1)=3\implies y=-4[/tex]
[tex] x=2 \implies y+1=3 \implies y=2[/tex]
[tex] x=-2 \implies -3(y+1)=3\implies y=-2[/tex]
[tex] x=4 \implies 3(y+1)=3 \implies y=0[/tex]
[tex]\hfill{\boxdot}[/tex]
