1. The problem statement, all variables and given/known data if an entire function satisfies f(z+i)=f(z) and f(z+1)=f(z), must the function be constant? 2. Relevant equations 3. The attempt at a solution It's true that f(0) = f(k) = f(ik) where k is an integer. I'm wondering whether I can apply Liouville's theorem into this somehow or if it's not constant at all on how to construct a counterexample.