Question

Tìm n ϵ N, biết: 4n + 23 ⋮ 2n + 3

Answer 1

Do \(n\in N\Rightarrow2n+3\ge3\)

\(4n+23⋮2n+3\)

\(\Rightarrow4n+6+17⋮2n+3\)

Do \(4n+6=2\left(2n+3\right)⋮2n+3\)

\(\Rightarrow17⋮2n+3\)

\(\Rightarrow2n+3=Ư\left(17\right)=\left\{17\right\}\)

\(\Rightarrow2n+3=17\)

\(\Rightarrow n=7\)