a) Ta có: \(n+12⋮n+4\)
\(\Leftrightarrow n+4+8⋮n+4\)
mà \(n+4⋮n+4\)
nên \(8⋮n+4\)
\(\Leftrightarrow n+4\inƯ\left(8\right)\)
\(\Leftrightarrow n+4\in\left\{1;2;4;8;-1;-2;-4;-8\right\}\)
\(\Leftrightarrow n\in\left\{-3;-2;0;4;-5;-6;-8;-12\right\}\)
mà \(n\in N\)
nên \(n\in\left\{0;4\right\}\)
Vậy: Khi \(n\in\left\{0;4\right\}\) thì \(n+12⋮n+4\)
b) Ta có: \(5n-6⋮n\)
mà \(5n⋮n\)
nên \(-6⋮n\)
\(\Leftrightarrow n\inƯ\left(-6\right)\)
\(\Leftrightarrow n\in\left\{-1;-2;-3;-6;1;2;3;6\right\}\)
mà n>1
nên \(n\in\left\{2;3;6\right\}\)
Vậy: Khi \(n\in\left\{2;3;6\right\}\) thì \(5n-6⋮n\)
c) Ta có: \(3n+13⋮2n+3\)
\(\Leftrightarrow6n+26⋮2n+3\)
\(\Leftrightarrow6n+9+17⋮2n+3\)
mà \(6n+9⋮2n+3\)
nên \(17⋮2n+3\)
\(\Leftrightarrow2n+3\inƯ\left(17\right)\)
\(\Leftrightarrow2n+3\in\left\{1;-17;-1;17\right\}\)
\(\Leftrightarrow2n\in\left\{-2;-20;-4;14\right\}\)
\(\Leftrightarrow n\in\left\{-1;-10;-2;7\right\}\)
mà \(n\ge1\)
nên n=7
Vậy: Khi n=7 thì \(3n+13⋮2n+3\)
