Đáp án:
h. n=7
Giải thích các bước giải:
\(\begin{array}{l}
e.n + 12 \vdots n + 4\\
\to n + 4 + 8 \vdots n + 4\\
\to 8 \vdots n + 4\\
\to n + 4 \in U\left( 8 \right)\\
\to \left[ \begin{array}{l}
n + 4 = 8\\
n + 4 = 4\\
n + 4 = 2\\
n + 4 = 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
n = 4\\
n = 0\\
n = - 2\\
n = - 3
\end{array} \right.\\
f.3n + 40 \vdots n + 4\\
\to 3\left( {n + 4} \right) + 28 \vdots n + 4\\
\to 28 \vdots n + 4\\
\to n + 4 \in U\left( {28} \right)\\
\to \left[ \begin{array}{l}
n + 4 = 28\\
n + 4 = 14\\
n + 4 = 7\\
n + 4 = 4\\
n + 4 = 2\\
n + 4 = 1
\end{array} \right. \to \left[ \begin{array}{l}
n = 24\\
n = 10\\
n = 3\\
n = 0\\
n = - 2\\
n = - 3
\end{array} \right.\\
g.5n + 2 \vdots 2n + 9\\
\Leftrightarrow 10n + 4 \vdots 2n + 9\\
\to 5\left( {2n + 9} \right) - 41 \vdots 2n + 9\\
\to 41 \vdots 2n + 9\\
\to 2n + 9 \in U\left( {41} \right)\\
\to \left[ \begin{array}{l}
2n + 9 = 41\\
2n + 9 = 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
n = 16\\
n = - 4
\end{array} \right.\\
h.3n + 13 \vdots 2n + 3\\
\to 6n + 26 \vdots 2n + 3\\
\to 3\left( {2n + 3} \right) + 17 \vdots 2n + 3\\
\to 17 \vdots 2n + 3\\
\to 2n + 3 \in U\left( {17} \right)\\
\to \left[ \begin{array}{l}
2n + 3 = 17\\
2n + 3 = 1
\end{array} \right.\\
\to \left[ \begin{array}{l}
n = 7\\
n = - 1\left( l \right)
\end{array} \right.\left( {Do:n \ge 1} \right)\\
\to n = 7
\end{array}\)
