Question

Chứng minh n+5 chia hết cho n-3 (n thuộc Z)

Answer 1

\(n+5⋮n-3\)

\(\Rightarrow n-3+8⋮n-3\)

     \(n-3⋮n-3\)

\(\Rightarrow8⋮n-3\)

\(\Rightarrow n-3\inƯ\left(8\right)\)

     \(n\inℤ\Rightarrow n-3\inℤ\)

\(\Rightarrow n-3\in\left\{-1;1;-2;2;-4;4-8;8\right\}\)

\(\Rightarrow n\in\left\{2;4;1;5;-1;7;-5;11\right\}\)

Answer 2

\(n+5⋮n-3\)

\(\Leftrightarrow\left(n-3\right)+8⋮n-3\)

-Mà: \(n-3⋮n-3\Rightarrow8⋮n-3\)

\(\Leftrightarrow n-3\inƯ\left(8\right)\)

\(\Rightarrow.....\)