Question

Tìm số nguyên n

a)n+9\(⋮\)n+2

b)9-n \(⋮\)n-3

c)2n+7\(⋮\)n+1

d)3n+7\(⋮\)2n+1

Answer 1

\(a,n+9⋮n+2\)

\(\Rightarrow n+2+7⋮n+2\)

mà \(n+2⋮n+2\Rightarrow n+2\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)

\(n\in\left\{-1;-3;5;-9\right\}\)

Answer 2

\(b,2n+7⋮n+1\)

\(\Rightarrow2n+2+5⋮n+1\)

\(\Rightarrow2\left(n+1\right)+5⋮n+1\)

mà \(2\left(n+1\right)⋮n+1\Rightarrow5⋮n+1\)

\(\Rightarrow n+1\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

\(\Rightarrow n\in\left\{0;-2;4;-6\right\}\)