Đáp án: $ n\in\{-1, 0, -2, 1, -3, 2, -4\}$
Giải thích các bước giải:
Để $A\in Z$
$\to 2n^2+5n+8\quad\vdots\quad n^2+2n+2$
$\to 2(n^2+2n+2)+n+4\quad\vdots\quad n^2+2n+2$
$\to n+4\quad\vdots\quad n^2+2n+2$
$\to (n+4)(n-2)\quad\vdots\quad n^2+2n+2$
$\to n^2+2n-8\quad\vdots\quad n^2+2n+2$
$\to n^2+2n+2-10\quad\vdots\quad n^2+2n+2$
$\to 10\quad\vdots\quad n^2+2n+2$
$\to n^2+2n+2\in U(10)$
Mà $n^2+2n+2=(n+1)^2+1\ge 1$
$\to n^2+2n+2\in\{1, 2, 5, 10\}$
$\to n\in\{-1, 0, -2, 1, -3, 2, -4\}$
