Question

[trầnnmt]

Tìm số nguyên n sao cho (3n+24)⋮(n−4)3𝑛+24⋮𝑛−4.

Answer 1

[Akai Haruma]

Lời giải:

$3n+24\vdots n-4$

$\Rightarrow 3(n-4)+36\vdots n-4$

$\Rightarrow 36\vdots n-4$

$\Rightarrow n-4\in\left\{\pm 1; \pm 2; \pm 3; \pm 4; \pm 6; \pm 9; \pm 12; \pm 18; \pm 36\right\}$
$\Rightarrow n\in\left\{5; 3; 2; 6; 7; 1; 8; 0; 10; -2; 13; -5; 16; -8; 22; -14; 40; -32\right\}$