Why doesn't $f(z)=\sqrt z$ work as a counterexample to If $f(z)$ is not an entire function, then $g(z) = f^2(z)$ cannot be an entire function.
94190
Disproving the statement "If $f(z)$ is not an entire function, then $g(z) = f^2(z)$ is not entire.”
107518
Entire function $f$ such that $|f(z)| ≤ K |z|^3$ for $|z|\ge1$ and $f(z) = f(iz)$ for every $z∈C$
745
$F(x)$ versus $F[x]$ where $F$ is a field
53513
Why is it that in $\mathbb{F}_q \setminus 0$, there are exactly as many squares as non-squares?
60261
Is $\sqrt{x^2}=|x|$ or $=x$? Isn't $(x^2)^\frac12=x?$
66238
Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD
131424
which of the following is NOT a possible value of $(e^{f})''(0)$??
98356
There does not exist an entire function which satisfies $f({1\over n})={1\over 2^n}$?
133775
Is $\mathbb{Z}[\sqrt{-7}]$ a UFD or not?
90276
Is $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$ true?
25050
To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
133386
If $f$ is entire and $\lim_\limits{z\to\infty} \frac{f(z)}{z} = 0$ show that $f$ is constant
126989
Prove that $g(z)=\overline{f(z)}$ is complex diﬀerentiable at $a$ if and only if $f'(a) = 0$.
65548
Prove if f(z) is entire function s.t $|f(z)|\leq M|z|$ then $f(z)$ Is polynomial of degree $1$
148512
No analytic function $f$ has modulus $|f(z)|=1/\cosh(\Re z)$
114810
$n!$ is never a perfect square if $n\geq2$. Is there a proof of this that doesn't use Chebyshev's theorem?
20955
Let $f(z)$ be analytic on $\mathbb{D}$ = {${z\in\mathbb{C}:|z-1|<1}$} such that $f(1) = 1$, if $f(z) = f(z^2)$ for all $z\in\mathbb{D}$,