AHSME 1980 Problem 28

The polynomial $x^{2n}+1+(x+1)^{2n}$ is not divisible by $x^2+x+1$ if $n$ equals $\text{(A)} \ 17 \text{(B)} \ 20 \text{(C)} \ 21 \text{(D)} \ 64 \text{(E)} \ 65$