Bài 1:
\(n+5⋮n-2\)
\(\Rightarrow\left(n-2\right)+7⋮n-2\)
\(\Rightarrow7⋮n-2\)
\(\Rightarrow n-2\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
\(\Rightarrow n=\left\{\begin{matrix}n-2=-1\Rightarrow n=1\\n-2=1\Rightarrow n=3\\n-2=-7\Rightarrow n=-5\\n-2=7\Rightarrow n=9\end{matrix}\right.\)
\(\Rightarrow n=\left\{1;3;-5;9\right\}\)
\(2n+1⋮n-5\)
\(\Rightarrow2n-10+11=2\left(n-5\right)+11⋮n-5\)
\(\Rightarrow11⋮n-5\)
\(\Rightarrow n-5\inƯ\left(11\right)=\left\{\pm1;\pm11\right\}\)
\(\Rightarrow n=\left\{\begin{matrix}n-5=-1\Rightarrow n=4\\n-5=-11\Rightarrow n=-6\\n-5=1\Rightarrow n=6\\n-5=11\Rightarrow n=16\end{matrix}\right.\)
\(\Rightarrow n=\left\{4;-6;6;16\right\}\)
Bài 2:
\(S=1+2-3-4+5+6-7-8+...-99+100\)
\(S=1+\left(2-3-4+5\right)+\left(6-7-8+9\right)+\left(97-98-99+100\right)\)
\(S=1+0+0+...+0\)
\(S=1\)
