Showing that, for $|a|>3$ and $n\geq1$, the function $f(z)=e^z-az^n$ has exactly $n$ roots (all simple and different) in the open unit disc
57191
Show that if $a>e$, the equation $az^n=e^z$ admit $n$ roots in the unit disk - Rouché theorem
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
157487
Showing a polynomial having at least one integer root under certain conditions has precisely one integer root
14759
Prove that $ f(z) = 0 $ for all $ z \in \overline{D}(0,1) $.
14648
Show that $f_0 - f_1 + f_2 - \cdots - f_{2n-1} + f_{2n} = f_{2n-1} - 1$ when $n$ is a positive integer
155444
Show that entire function $f$ is a polynomial of degree at most $n$
116507
Very quick question: function extends to 1/z on the boundary of unit disc
115459
Proving this $F_{n+1} \cdot F_{n-1} - F^2_n = (-1)^n$ by induction
127547
Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.
115781
Proof about Holomorphic functions in the unit disc
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
101371
show that $f^{(3)}(c) \ge 3$ for $c\in(-1,1)$
156034
sufficient condition for a polynomial to have roots in $[0,1]$
123467
Prove that $f(z) = e^z$ maps $\mathbb{C} \setminus B $ onto $\mathbb{C} \setminus \{0\}$.
82079
Holomorphic function satisfying $f^{-1}(\Bbb R)=\Bbb R$ is of the form $f(z)=az+b$
84697
Show that if $|f(z)| \leq M |z|^n$ then $f$ is a polynomial max degree n
145509
Prove the roots of $p(z)+z^n\bar{p}(\frac{1}{z})$ lie on the unit circle