# Homework Help: Complex analysis/entire function question

1. Sep 21, 2011

### nugget

1. The problem statement, all variables and given/known data

Suppose f is an entire function, satisfying

f(z + a) = f(z) = f(z + b), for all z $\in$ C; where a; b are nonzero, distinct complex numbers.

Prove that f is constant.

2. Relevant equations

Loville's theorem: if f is bounded & entire, then f is constant.

3. The attempt at a solution

where would I begin to prove this function is bounded? any hint would be appreciated!

2. Sep 21, 2011

### lineintegral1

Yes, show that the function is bounded. This isn't particularly hard to do because it is periodic!