3. Let $n$ be a natural number. Then the divisibility of $n^{2}+n+2$ is ( ).
(A) Neither divisible by 2 nor by 5
(B) Divisible by 2, but not by 5
(C) Not divisible by 2, but divisible by 5
(D) Divisible by both 2 and 5
3. (B).

Since $n^{2}+n=n(n+1)$, and $n(n+1)$ is divisible by 2, therefore, $n^{2}+n+2$ is divisible by 2. Also, the unit digit of $n(n+1)$ can only be $0, 2, 6$, then the unit digit of $n^{2}+n+2$ can only be $2, 4, 8$, so it cannot be divisible by 5.