Question

Exercitiul 2 , va rog . multumesc anticipat

Answer 1

Răspuns:

$(x, y)\in\left\{(0,-4),(2,2),(-2,3),(4,0)\right\}$

Explicație pas cu pas:

$\dfrac{x-1}{3}=\dfrac{1}{y+1}\iff (x-1)(y+1)=3.$

Fiind 3 un număr ireductibil, avem că

$(x-1)\mid 3 \implies x-1\in\left\{-1,1,-3,3\right\}$ adică $x\in\left\{0,2,-2,4\right\}.$

$x=0 \implies -(y+1)=3\implies y=-4$

$x=2 \implies y+1=3 \implies y=2$

$x=-2 \implies -3(y+1)=3\implies y=-2$

$x=4 \implies 3(y+1)=3 \implies y=0$

$\hfill{\boxdot}$