Question

tìm n thuộc N biết 

a) 3.n :: n + 2

b) ( 3.n+ 1 ) :: n - 2

Answer 1

1.

$3n\vdots n+2$

$\Rightarrow 3(n+2)-6\vdots n+2$

$\Rightarrow 6\vdots n+2$

$\Rightarrow n+2\in\left\{\pm 1; \pm 2; \pm 3; \pm 6\right\}$

$\Rightarrow n\in \left\{-1; -3; 0; -4; 1; -5; 4; -8\right\}$

Do $n\in\mathbb{N}\Rightarrow n\in\left\{0; 1; 4\right\}$

Answer 2

2.

$3n+1\vdots n-2$

$\Rightarrow 3(n-2)+7\vdots n-2$

$\Rightarrow 7\vdots n-2$

$\Rightarrow n-2\in\left\{\pm 1; \pm 7\right\}$

$\Rightarrow n\in\left\{1; 3; -5; 9\right\}$

Do $n\in\mathbb{N}$ nên $n\in\left\{1;3;9\right\}$