Đáp án:
a. \(\left[ \begin{array}{l}
n = 5\\
n = - 3\\
n = 3\\
n = - 1\\
n = 2\\
n = 0
\end{array} \right.\)
b. \(\left[ \begin{array}{l}
n = 3\\
n = - 7\\
n = - 1\\
n = - 3
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a.n + 3 \vdots n - 1\\
\Leftrightarrow n - 1 + 4 \vdots n - 1\\
\Leftrightarrow 4 \vdots n - 1\\
\Leftrightarrow n - 1 \in U\left( 4 \right)\\
\Leftrightarrow \left[ \begin{array}{l}
n - 1 = 4\\
n - 1 = - 4\\
n - 1 = 2\\
n - 1 = - 2\\
n - 1 = 1\\
n - 1 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
n = 5\\
n = - 3\\
n = 3\\
n = - 1\\
n = 2\\
n = 0
\end{array} \right.\\
b.2n - 1 \vdots n + 2\\
\Leftrightarrow 2\left( {n + 2} \right) - 5 \vdots n + 2\\
\Leftrightarrow 5 \vdots n + 2\\
\Leftrightarrow n + 2 \in U\left( 5 \right)\\
\Leftrightarrow \left[ \begin{array}{l}
n + 2 = 5\\
n + 2 = - 5\\
n + 2 = 1\\
n + 2 = - 1
\end{array} \right. \to \left[ \begin{array}{l}
n = 3\\
n = - 7\\
n = - 1\\
n = - 3
\end{array} \right.
\end{array}\)
