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## Homework Statement

if an entire function satisfies f(z+i)=f(z) and f(z+1)=f(z), must the function be constant?

## Homework Equations

## 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.