Is f(z) = e^(z^2) for all z in C?

[Matt100]

Assume |f(z)| >= 1/3|e^(z^2)| for all z in C and that f(0) = 1 and that f(z) is entire. Prove that f(z) = e^(z^2) for all z in C.

How do you start for this.

 

[FactChecker]

Let g(z) = e^(z^2) and consider the function g(z)/f(z). Show that it is entire and has a bounded modulous. You should be able to continue from there.