Giải thích các bước giải:
a.Ta có:
$n^2-7\quad\vdots\quad n+3$
$\to (n^2-3n)+(3n-9)+2\quad\vdots\quad n+3$
$\to n(n-3)+3(n-3)+2\quad\vdots\quad n+3$
$\to 2\quad\vdots\quad n+3$
$\to n+3\in U(2)$
$\to n+3\in\{2,1,-1,-2\}$
$\to n\in\{-1,-2,-4,-5\}$
b.Ta có:
$n+3\quad\vdots\quad n^2-7$
$\to (n+3)(n-3)\quad\vdots\quad n^2-7$
$\to n(n+3)-3(n+3)\quad\vdots\quad n^2-7$
$\to n^2+3n-3n-9\quad\vdots\quad n^2-7$
$\to n^2-9\quad\vdots\quad n^2-7$
$\to n^2-7-2\quad\vdots\quad n^2-7$
$\to 2\quad\vdots\quad n^2-7$
$\to n^2-7\in U(2)$
$\to n^2-7\in\{1,2,-1,-2\}$
$\to n^2\in\{8,9,6,5\}$
$\to n^2=9$ vì $n^2$ là số chính phương
$\to n=\pm3$
