Giải thích các bước giải:
x,y nguyên nên: (x-1) ² >0 và (x-1) ² nguyên
Ta có: -16= 16. (-1)=4. (-4) = 1. (-16)
$\begin{array}{l}
+ TH1:\left\{ \begin{array}{l}
{\left( {x - 1} \right)^2} = 16\\
y + 3 = - 1
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x - 1 = 4\\
x - 1 = - 4
\end{array} \right.\\
y = - 4
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x = 5\\
x = - 3
\end{array} \right.\\
y = - 4
\end{array} \right.\\
+ TH2:\left\{ \begin{array}{l}
{\left( {x - 1} \right)^2} = 4\\
y + 3 = - 4
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x - 1 = 2\\
x - 1 = - 2
\end{array} \right.\\
y = - 7
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x = 3\\
x = - 1
\end{array} \right.\\
y = - 7
\end{array} \right.\\
+ TH3:\left\{ \begin{array}{l}
{\left( {x - 1} \right)^2} = 1\\
y + 3 = - 16
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x - 1 = 1\\
x - 1 = - 1
\end{array} \right.\\
y = - 19
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x = 2\\
x = 0
\end{array} \right.\\
y = - 19
\end{array} \right.\\
Vay\,\left( {x;y} \right) = \left\{ \begin{array}{l}
\left( {5; - 4} \right);\left( { - 3; - 4} \right);\left( {3; - 7} \right);\\
\left( { - 1; - 7} \right);\left( {2; - 19} \right);\left( {0; - 19} \right)
\end{array} \right\}
\end{array}$
