Given two entire functions $f_1,f_2$ without common zeros, prove that one can find some entire functions $g_1,g_2$ such that $f_1g_1+f_2g_2=1$
10003
Given two holomorphic functions on a region find two other such that...
53024
$f(x)f(1/x)=f(x)+f(1/x)$
107765
Prove that there exists two roots in $[-1,1]$
4296
If $f,g$ are entire functions and$\ fg\equiv 0$ then either $f \equiv 0$ or $g\equiv0. $
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
58178
Property of Entire Functions
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
20907
Entire function, Liouville and zeroes
95288
Prove that, $f'(0) \ge -\sqrt{2}$ for a function $f$ satisfying some conditions on $(-1,1)$.
69219
Prove there is a point $z\in[a,b]$ at which $f(z)=\frac{f(x_1)+f(x_2)+\cdots+f(x_k)}{k}$
98399
Suppose $f$ and $g$ are entire functions, and $|f(z)| \leq |g(z)|$ for all $z \in \mathbb{C}$, Prove that $f(z)=cg(z)$.
127887
Existence of a meromorphic functions $f(z)$ such that $|f(z)|\geq |z|$.
74051
No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
50552
find functions that $f(m+k)=f(mk-n)$
146572
Prove that between any two roots of $f$ there exists at least one root of $g$
74245
Characterizing non-constant entire functions with modulus $1$ on the unit circle
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$