Can someone help me in this problem?
Let $p,q$ be prime numbers with $p < q$.
- There exists $m \in \mathbb{Z}^+$ for which $1+p+p^2+...+p^m$ is a power of $q$.
- There exists $n \in \mathbb{Z}^+$ for which $1+q+q^2+...+q^n$ is a power of $p$.
Prove that $p = 2, q = 2^t - 1$, with $t$ being a prime number.
