Câu hỏi của Trâm Nguyễn

Question

Tìm số tự nhiên n :

3n+10 ⋮ n-1

Nguyễn Việt Lâm · Accepted Answer

$3n+10⋮n-1\Rightarrow3n-3+13⋮n-1$

$\Rightarrow3\left(n-1\right)+13⋮n-1$

Do $3\left(n-1\right)⋮n-1\Rightarrow13⋮n-1$

$\Rightarrow n-1=Ư\left(13\right)=\left\{-13;-1;1;13\right\}$

$\Rightarrow n=\left\{-12;0;2;14\right\}$

Do n là số tự nhiên $\Rightarrow n=\left\{0;2;14\right\}$

Câu trả lời:

$3n+10⋮n-1\Rightarrow3n-3+13⋮n-1$

$\Rightarrow3\left(n-1\right)+13⋮n-1$

Do $3\left(n-1\right)⋮n-1\Rightarrow13⋮n-1$

$\Rightarrow n-1=Ư\left(13\right)=\left\{-13;-1;1;13\right\}$

$\Rightarrow n=\left\{-12;0;2;14\right\}$

Do n là số tự nhiên $\Rightarrow n=\left\{0;2;14\right\}$