Tìm cặp số nguyên x; y biết: xy – x – y  2

Lời giải:

xy – x – y = 2

xy – x – y + 1 = 3

x(y – 1) – 1(y – 1) = 3

(x – 1)(y – 1) = 3

Suy ra (x – 1) và (y – 1) Î Ư(3) = {±1; ±3}

TH1: \(\left\{ \begin{array}{l}x - 1 = 1\\y - 1 = 3\end{array} \right.\,\,n\^e n\,\,\left\{ \begin{array}{l}x = 2\\y = 4\end{array} \right.\)

TH2: \(\left\{ \begin{array}{l}x - 1 = - 1\\y - 1 = - 3\end{array} \right.\,\,n\^e n\,\,\left\{ \begin{array}{l}x = 0\\y = - 2\end{array} \right.\)

TH3: \(\left\{ \begin{array}{l}x - 1 = 3\\y - 1 = 1\end{array} \right.\,\,n\^e n\,\,\left\{ \begin{array}{l}x = 4\\y = 2\end{array} \right.\)

TH4: \(\left\{ \begin{array}{l}x - 1 = - 3\\y - 1 = - 1\end{array} \right.\,\,n\^e n\,\,\left\{ \begin{array}{l}x = - 2\\y = 0\end{array} \right.\)