I've encountered the following question in my research:
Let $A$ be a subset of $\mathbb{Z}/n\mathbb{Z}$. Let me call $A$ "sum-free" if there is no solution to $x+y=z$ for $x,y,z \in A$ with distinct $x$ and $y$. The addition is of course mod $n$.
Question: For which $n$ is the set $A = \{2^x \!\!\mod n: x>0\}$ (the set of powers of $2$) sum-free? I'm assuming that $n$ is odd.
Does anyone have an idea how to approach this question?