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So the problem states that if $f(z)$ is entire, and satisfies the relation $f(z+i) = f(z)$ and $f(z+1) = f(z)$, show that $f(z)$ is constant. So I was thinking that since any point in $\mathbb{C}$ can be written as $\alpha * 1 + \beta * i $ we can say that $f(z + z_0) = f(z) $ in which case it is constant, but I'm having trouble breaking down the steps, and using the fact that f is entire, which makes me feel like I'm missing something. What should I review to figure this out?

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    Might try showing $f(\mathbb{C})$ is the same as $f(I\times I)$, where $I$ is the unit interval. Then of course since $I\times I$ is compact, the image is bounded, and Liouville saves the day.2011-05-04
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    max modulus principle2011-05-04
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    Thanks @yoyo, that was really helpful to review as well. It applies to another question that I was also stuck on.2011-05-04

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