1. a) \(\left(n+15\right)⋮\left(n+2\right)\)
\(\Rightarrow\left[n+15-\left(n+2\right)\right]⋮\left(n+2\right)\)
\(\Rightarrow\left[n+15-n-2\right]⋮\left(n+2\right)\)
\(\Rightarrow13⋮\left(n+2\right)\)
\(\Rightarrow\left(n+2\right)\inƯ_{\left(13\right)}=\left\{\pm1;\pm13\right\}\)
\(\Rightarrow n\in\left\{...\right\}\)
b) \(\left(3n+17\right)⋮\left(n+1\right)\)
\(\Rightarrow\left(3n+17\right)⋮3\left(n+1\right)\)
\(\Rightarrow\left(3n+17\right)⋮\left(3n+3\right)\)
\(\Rightarrow\left[\left(3n+17\right)-\left(3n+3\right)\right]⋮\left(n+1\right)\)
\(\Rightarrow\left[3n+17-3n-3\right]⋮\left(n+1\right)\)
\(\Rightarrow14⋮\left(n+1\right)\)
\(\Rightarrow\left(n+1\right)\inƯ_{\left(14\right)}=\left\{\pm1;\pm2;\pm7;\pm14\right\}\)
\(\Rightarrow n\in\left\{...\right\}\)
a, \(n+15⋮n+2\)
\(\Rightarrow n+2+13⋮n+2\)
\(\Rightarrow n+2\inƯ\left(13\right)=\left\{\pm1;\pm13\right\}\)
+ n + 2 = 1 \(\Rightarrow\)n = -1
+ n + 2 = -1 \(\Rightarrow\)n = -3
+ n + 2 = -13 \(\Rightarrow\)n = -15
+ n + 2 = 13 \(\Rightarrow\)n = 11
b, \(3n+17⋮n+1\)
\(\Rightarrow3\left(n+1\right)+14⋮n+1\)
\(\Rightarrow n+1\inƯ\left(14\right)=\left\{\pm1;\pm2;\pm7;\pm14\right\}\)
+ n + 1 = 1\(\Rightarrow\)n = 0
+ n + 1 = -1\(\Rightarrow\)n = -2
+ n + 1 = 2\(\Rightarrow\)n = 1
+ n + 1 = -2\(\Rightarrow\)n = -3
+ n + 1 = 7\(\Rightarrow\)n = 6
+ n + 1 = -7\(\Rightarrow\)n = -8
+ n + 1 = 14\(\Rightarrow\)n = 13
+ n + 1 = -14\(\Rightarrow\)n = -15