For this problem, I decided to factor out a z^(3m) and get z^3m (z^2 + z + 1) - z^3m + 1. The first part is divisible by z^2 + z + 1, so I need to prove that 1 - z^3m is also divisible by z^2 + z + 1. Factoring, I got (1 - z^m)(z^2m + z^m + 1). This is similar to z^2 + z + 1, but I do not know what to do now. Is this a bad strategy? Is there a better way to approach this problem? Thank you.