$n^2 + 7 \vdots n+3$
=> $n^2 + 3n - 3n+ 7 \vdots n+3$
=> $n(n+3) - 3n+7 \vdots n+3$
Vì $n(n+3) \vdots n+3$ nên $-3n+7 \vdots n+3$
=> $-3n-9+16 \vdots n+3$
=> $-3(n+3)+16 \vdots n+3$
Vì $-3(n+3) \vdots n+3$ nên $16 \vdots n+3$
=> $n+3 \in Ư(16)= \{ \pm 1; \pm 2; \pm 4; \pm 8; \pm 16\}$
=> $n \in \{ -2; -4; -1; -5; 1; -7; 5; -11; 13; -19\}$