28 If and only if $n$ is divisible by $k$, the polynomial $x^{2 n}+1+(x+1)^{2 n}$ is not divisible by $x^{2}+x+1$, then the value of $k$ is
A. 2
B. 3
C. 6
D. A conclusion different from A, B, and C
28 B. If $n$ is divisible by 3. Let $w$ be a complex cube root of 1, then $w^{2 n}+1+(w+1)^{2 n}=3 \neq 0$. Therefore, $x^{2 n}+1+(x+1)^{2 n}$ is not divisible by $x^{2}+x+1$.
If $n$ is not divisible by 3, then $w^{2 n}+1+(w+1)^{2 n}=w^{2 n}+1+\left(w^{2}\right)^{2 n}=0$, so $x^{2 n}+1+(x+1)^{2 n}$ is divisible by $x^{2}+x+1$.