Giải thích các bước giải:
a.Để $3n^3+10n^2-5\quad \vdots\quad 3n+1$
$\rightarrow (3n^3+n^2)+(9n^2-1)-4\quad \vdots\quad 3n+1$
$\rightarrow n^2(3n+1)+(3n-1)(3n+1)-4\quad \vdots\quad 3n+1$
$\rightarrow 4\quad \vdots\quad 3n+1$
$\rightarrow 3n+1\in U(4)=\{1,2,4,-1,-2,-4\}$
$\rightarrow n\in\{0, 1,-1\}$ do $n\in Z$
b.Để
$10n^2+n-10\quad \vdots\quad n-1$
$\rightarrow 10n^2-10+n-1+1\quad \vdots\quad n-1$
$\rightarrow 10(n-1)(n+1)+(n-1)+1\quad \vdots\quad n-1$
$\rightarrow 1\quad \vdots\quad n-1$
$\rightarrow n-1\in\{-1,1\}$
$\rightarrow n\in\{0,2\}$