Complex analysis/entire function question

[nugget]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

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

 

[lineintegral1]

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