Take $f$ and entire function such that $f(z) = f(z+1)=f(z+\sqrt{2})$, then it is constant
62268
Doubly periodic entire function with periods that are linearly independent over $\mathbb{Q}$ is constant.
118136
Finding univalent function with $f(z_1)=z_2$
96050
$f$ an analytic function on $\mathbb{C}$ which takes values in $\mathbb{C}\backslash(-\infty,0]$ implies constant
27772
Let $f$ be an analytic function such that $\operatorname{Im}(f(z))=\operatorname{Re}(f(z))^2$. Prove that $f$ is constant.
75638
Let $u:\mathbb{C}\rightarrow\mathbb{R}$ be a harmonic function such that $0\leq f(z)$ for all $ z \in \mathbb{C}$. Prove that $u$ is constant.
74202
Show that $|f(z_1)|=|f(z_2)|≤|z_1|^2=|z_2|^2$.
153855
Complex analysis, showing a function is constant
148981
Entire $f$ and $g$ constant if $e^{f(z)}+e^{g(z)}=1$
142494
Functions $f(x)/g(x), g(x)/h(x),h(x)/f(x)$ are constant
8179
If $f$ is entire and $|f|\geq 1$, then show $f$ is constant.
62640
Show a given analytic function is constant
94597
$f, g$ entire functions with $f^2 + g^2 \equiv 1 \implies \exists h $ entire with $f(z) = \cos(h(z))$ and $g(z) = \sin(h(z))$
86517
If $|f(z)|\le |g(z)|$, can we say $f$ is constant?
63255
Proving an entire, complex function with below bounded modulus is constant.
97371
Proving a function is constant, under certain conditions?
56127
Prove a function is constant under certain conditions
147270
Entire function. Prove that $f(\bar{z})=\overline{f(z)}, \forall z\in C$