Let $p$ be a prime number, I think when $p^2+p+1=q^a$, where $q$ is a prime number, then $a=1$. But I can't prove it. Is it true?



What is prime power of this equation of p?
This question is answered (affirmatively and somewhat more generally) in the following paper: Chat Yin Ho, [Projective planes with a regular collineation group and a question about powers of a prime](http://www.sciencedirect.com/science/article/pii/S0021869383710094), J. Algebra 154 (1993), no. 1, 141–151. The proof there uses the ring of Eisenstein integers. (The issue is available online via Open Access).


