1980 AMC 12 Problem 28

Evaluate the polynomial at a nonreal cube root of unity $\omega$

Use $1+\omega=-\omega^2$ and consider $n$ modulo $3$

Let $\omega^2+\omega+1=0.$ Since $1+\omega=-\omega^2,$ the polynomial evaluated at $\omega$ is $$\omega^{2n}+1+\omega^{4n}.$$ This is $0$ unless $\omega^{2n}=1,$ in which case it is $3.$ The latter occurs exactly when $n$ is divisible by $3.$ Among the choices only $21$ is divisible by $3,$ so that is the value for which divisibility fails.

Therefore, the correct answer is C.