Giải thích các bước giải:
Bài 5:
a.Để $\dfrac{3n-2}{n-3}\in Z$
$\to 3n-2\quad\vdots\quad n-3$
$\to 3n-9+7\quad\vdots\quad n-3$
$\to 3(n-3)+7\quad\vdots\quad n-3$
$\to 7\quad\vdots\quad n-3$
$\to n-3\in\{1,7,-1,-7\}$
$\to n\in\{4,10,2,-4\}$
b.Lập luận tương tự câu a
$\to 3n-1\quad\vdots\quad 2n+1$
$\to 2(3n-1)\quad\vdots\quad 2n+1$
$\to 6n-2\quad\vdots\quad 2n+1$
$\to 6n+3-5\quad\vdots\quad 2n+1$
$\to 3(2n+1)-5\quad\vdots\quad 2n+1$
$\to 5\quad\vdots\quad 2n+1$
$\to 2n+1\in\{1,5,-1,-5\}$
$\to n\in\{0,2,-1,-3\}$
c.Tương tự
$\to 2n-3\quad\vdots\quad 3n-2$
$\to 3(2n-3)\quad\vdots\quad 3n-2$
$\to 6n-9\quad\vdots\quad 3n-2$
$\to 6n-4-5\quad\vdots\quad 3n-2$
$\to 2(3n-2)-5\quad\vdots\quad 3n-2$
$\to 5\quad\vdots\quad 3n-2$
$\to 3n-2\in\{-5,1\}$ vì $3n-2$ chia 3 dư 2
$\to n\in\{-1, 1\}$
