D=4x-6/2x+1 là số nguyên

`D = (4x -6)/(2x +1)`

`= (4x + 2 - 8)/(2x +1 )`

`= (2(2x +1) - 8)/(2x +1)`

Ta có `:`

` 2(2x +1) \vdots 2x +1`

Để ` (4x -6)/(2x +1) in ZZ`

`-> -8 \vdots 2x +1`

hay `2x +1 in Ư(8) = { +-1;+-2;+-4;+-8}`

Ta có bảng sau `:`

\begin{array}{|c|c|c|}\hline \text{2x +1}&\text{1}&\text{-1}&\text{2}&\text{-2}&\text{-4}&\text{4}&\text{-8}&\text{8}\\\hline \text{}x&\text{0}&\text{-1}&\text{1/2}&\text{-3/2}&\text{-5/2}&\text{3/2}&\text{-9/2}&\text{7/2}\\\hline \end{array}

Vậy `x in { 0;-1;1/2;-3/2;-5/2;3/2;-9/2;7/2}` thì `(4x -6)/(2x +1) in ZZ`