Đáp án:
$\begin{array}{l}
a)\frac{{13}}{{x + 5}} \in N*\\
\Rightarrow 13 \vdots \left( {x + 5} \right)\\
\Rightarrow \left[ \begin{array}{l}
x + 5 = 1\\
x + 5 = 13
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = - 4\left( {tm} \right)\\
x = 9\left( {tm} \right)
\end{array} \right.\\
Vay\,x = - 4\,hoac\,x = 9\\
b)\left( {x - 1} \right)\left( {y + 2} \right) = 7 = 1.7 = \left( { - 1} \right).\left( { - 7} \right)\\
\Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x - 1 = 1\\
y + 2 = 7
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 1 = 7\\
y + 2 = 1
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 1 = - 1\\
y + 2 = - 7
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 1 = - 7\\
y + 2 = - 1
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
x = 2;y = 5\\
x = 8;y = - 1\\
x = 0;y = - 9\\
x = - 6;y = - 3
\end{array} \right.\\
Vay\,\left( {x;y} \right) = \left\{ {\left( {2;5} \right);\left( {8; - 1} \right);\left( {0; - 9} \right);\left( { - 6; - 3} \right)} \right\}\\
B4)\\
\overline {aaa} = 100a + 10a + a\\
= 111.a\\
= 37.3.a \vdots 37\\
\Rightarrow \overline {aaa} \vdots 37
\end{array}$
Vậy số có dạng aaa luôn là bội của 37
