a/ \(4n+5⋮n\)
Mà \(n⋮n\)
\(\Leftrightarrow\left\{{}\begin{matrix}4n+5⋮n\\4n⋮n\end{matrix}\right.\)
\(\Leftrightarrow5⋮n\)
\(\Leftrightarrow n\inƯ\left(5\right)\)
\(\Leftrightarrow n\in\left\{1;5;-1;-5\right\}\)
Vậy ...
b/ \(38+3n⋮n\)
Mà \(n⋮n\)
\(\Leftrightarrow\left\{{}\begin{matrix}38+3n⋮n\\3n⋮n\end{matrix}\right.\)
\(\Leftrightarrow38⋮n\)
\(\Leftrightarrow n\inƯ\left(38\right)\)
\(\Leftrightarrow n\in\left\{\pm1;\pm38;\pm2;\pm19\right\}\)
Vậy ...
c/ \(3n+4⋮n-1\)
Mà \(n-1⋮n-1\)
\(\Leftrightarrow\left\{{}\begin{matrix}3n+4⋮n-1\\3n-3⋮n-1\end{matrix}\right.\)
\(\Leftrightarrow7⋮n-1\)
\(\Leftrightarrow n-1\inƯ\left(7\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}n-1=1\-1=7\-1=-1\-1=-7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}n=2\=8\=0\=-6\end{matrix}\right.\)
Vậy ...
d/ \(2n-1⋮16-3n\)
Mà \(16-3n⋮16-3n\)
\(\Leftrightarrow\left\{{}\begin{matrix}6n-3⋮16-3n\\-6n+32⋮16-3n\end{matrix}\right.\)
\(\Leftrightarrow29⋮16-3n\)
\(\Leftrightarrow16-3n\inƯ\left(29\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}16-3n=1\\16-3n=29\\16-3n=-1\\16-3n=-29\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=5\=-\dfrac{13}{3}\=-\dfrac{17}{3}\=15\end{matrix}\right.\)
Vậy ..
