tìm tất cả các cặp số nguyên x,y sao cho xy-2x-y=1.cần gấp .ai nhanh nhất mình đánh giá 5 sao

`xy - 2x - y = 1`

`⇒ x . ( y - 2 ) - y = 1`

`⇒ x . ( y - 2 ) - y + 2 = 1 + 2`

`⇒ x . ( y - 2 ) - ( y - 2 ) = 3`

`⇒ ( y - 2 ) ( x - 1 ) = 3`

Do `x , y ∈ Z ⇒ y - 2 , x - 1 ∈ Z`

`⇒ ( x - 1 ) ( y - 2 ) = 1 . 3 = ( - 1 ) . ( - 3 )`

Ta có bảng sau `:` 

\begin{array}{|c|c|c|}\hline \text{x - 1}&\text{1}&\text{3}&\text{- 1}&\text{- 3}\\\hline \text{y - 2}&\text{3}&\text{1}&\text{- 3}&\text{- 1}\\\hline \text{x}&\text{2}&\text{4}&\text{0}&\text{- 2}\\\hline \text{y}&\text{5}&\text{3}&\text{- 1}&\text{1}\\\hline\end{array}

Vậy `, ( x ; y ) ∈ { ( 2 ; 5 ) ; ( 4 ; 3 ) ; ( 0 ; - 1 ) ; ( - 2 ; 1 ) }`