# An entire function with two periods

Can anybody help me with this question:

If $f(z)$ is an entire periodic function and it has to periods $2$ and $2i$, how can I find all other periods?

-

If the function is entire, and has periods $2$ and $2i$, then it is bounded, and by Liouville, it is then a constant, so that any non-zero complex number is a period.