Thịnh làm lộn rùi kìa
$\begin{array}{l}
{x^2} + 2x - 2y - {y^2} = 2011\\
\Leftrightarrow {x^2} + 2x + 1 - \left( {{y^2} + 2y + 1} \right) = 2011\\
\Leftrightarrow {\left( {x + 1} \right)^2} - {\left( {y + 1} \right)^2} = 2011\\
\Leftrightarrow \left( {x - y} \right)\left( {x + y + 2} \right) = 2011
\end{array}$
Mà 2011 là SNT
$ \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
\left( {x - y} \right) = 1\\
\left( {x + y + 2} \right) = 2011
\end{array} \right.\\
\left\{ \begin{array}{l}
\left( {x - y} \right) = 2011\\
\left( {x + y + 2} \right) = 1
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x = 1005\\
y = 1004
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 1005\\
y = - 1004
\end{array} \right.
\end{array} \right.$
Mà x,y nguyên => (x;y)=(1005;1004)