Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
a.\left( {n + 5} \right) \vdots \left( {n - 3} \right) \Leftrightarrow (n - 3 + 8) \vdots \left( {n + 3} \right)\\
\Leftrightarrow 8 \vdots \left( {n + 3} \right) \Leftrightarrow \left( {n + 3} \right) \in U\left( 8 \right)\\
\Leftrightarrow \left[ \begin{array}{l}
n + 3 = 8\\
n + 3 = - 8\\
n + 3 = 4\\
n + 3 = - 4\\
n + 3 = 2\\
n + 3 = - 2\\
n + 3 = 1\\
n + 3 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
n = 5\\
n = - 11\\
n = 1\\
n = - 7\\
n = - 1\\
n = - 5\\
n = - 2\\
n = - 4
\end{array} \right.\\
b.\left( {4n - 5} \right) \vdots \left( {n - 3} \right)\\
\Leftrightarrow (4n - 12 + 7) \vdots \left( {n - 3} \right)\\
\Leftrightarrow 7 \vdots \left( {n - 3} \right)\\
\Leftrightarrow \left( {n - 3} \right) \in U\left( 7 \right)\\
\Leftrightarrow \left[ \begin{array}{l}
n - 3 = 7\\
n - 3 = - 7\\
n - 3 = 1\\
n - 3 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
n = 10\\
n = - 4\\
n = 4\\
n = 2
\end{array} \right.\\
c.\left( {n + 7} \right) \vdots \left( {n - 2} \right) \Leftrightarrow \left( {n - 2 + 9} \right) \vdots \left( {n - 2} \right)\\
\Leftrightarrow 9 \vdots \left( {n - 2} \right) \Leftrightarrow \left( {n - 2} \right) \in U\left( 9 \right)\\
\Leftrightarrow \left[ \begin{array}{l}
n - 2 = 9\\
n - 2 = - 9\\
n - 2 = 3\\
n - 2 = - 3\\
n - 2 = 1\\
n - 2 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
n = 11\\
n = - 7\\
n = 5\\
n = - 1\\
n = 3\\
n = 1
\end{array} \right.
\end{array}\)
