query: Let $f(z) = f(z^2)$, for all $z\in\mathbb{D}$ with $f(1) = 1$, then which of the following is incorrect?
positive_passages.docid: 20955
positive_passages.text: 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 $z\in\mathbb{D}$,
negative_passages.docid: 60348
negative_passages.text: How do I prove $F(a)=F(a^2)?$
negative_passages.docid: 101448
negative_passages.text: Is $\sin^2(z) + \cos^2(z)=1$ still true for $z \in \Bbb{C}$?
negative_passages.docid: 155531
negative_passages.text: Entire functions such that $f(z+\lambda_1)=af(z) \; , \; f(z+\lambda_2)=bf(z) $
negative_passages.docid: 77074
negative_passages.text: If $ f(f(f(x)))=x$, does$ f(x)=x$ necessarily follow?
negative_passages.docid: 82229
negative_passages.text: Show if complex function $f(z)$ contains all real coefficients then $f(\bar z)$ = $\bar {f(z)}$
negative_passages.docid: 149328
negative_passages.text: A function such that $f:\mathbb C \to \mathbb C$ such that $f(z)f(iz)=z^2$ satisfies $f(z)+f(-z)=0$.(MADHAVA-2020)
negative_passages.docid: 13794
negative_passages.text: $|z_{1} + z_{2}| = |z_{1} - z_{2}| \implies z_{1}/z_{2}$ is Imaginary
negative_passages.docid: 50012
negative_passages.text: $f: [a,b] \to \mathbb{R}$, $f(a) = f(b)$. Show $\exists c \in [a, \frac{a+b}{2} ]$ with $f(c)=f(c+\frac{b-a}{2})$
negative_passages.docid: 84510
negative_passages.text: If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
negative_passages.docid: 148981
negative_passages.text: Entire $f$ and $g$ constant if $e^{f(z)}+e^{g(z)}=1$
negative_passages.docid: 38568
negative_passages.text: Finding the number of zeros of $f(z) = z^n$ if $|f(z)| < 1 $ for all $z$ with $|z|=1$.
negative_passages.docid: 133636
negative_passages.text: Is $\mathbb Z[X]/(X^2-1)$ a domain?
negative_passages.docid: 78118
negative_passages.text: Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
negative_passages.docid: 16559
negative_passages.text: Difference between $\mathbb{Z}/n\mathbb{Z}$ and $\mathbb{Z}_n$
negative_passages.docid: 76285
negative_passages.text: Suppose $f$ is entire and $|f(z)| \leq 1/|Re z|^2$ for all $z$. Show that $f $ is identically $0$.
negative_passages.docid: 124346
negative_passages.text: Where is $f(z)=\Re (z)$ differentiable?