Prove $f(z)=z^2+\cos(z)$ has a zero in $\mathbb{C}$
105062
Prove that the range of the entire function $z^2+\cos(z)$ is all of $\mathbb{C}$.
61987
$x^2+1=0$ in $\mathbb{Z}_7$
88271
Prove the exsistence of 3 zero points of a function
71708
Proving that $\left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right) \lvert f(z) \rvert^2 = 4 \lvert f'(z) \rvert^2$
81921
If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
92537
Prove that $f(x)\in \mathbb{Z}[x]$ such that $f(0)$ and $f(1)$ are odd has no integer roots
69219
Prove there is a point $z\in[a,b]$ at which $f(z)=\frac{f(x_1)+f(x_2)+\cdots+f(x_k)}{k}$
111076
If $f$ is non-constant and entire, prove that there exists a $z_0 \in C$ such that $f(z_0)$ is a positive real number
155165
Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
60348
How do I prove $F(a)=F(a^2)?$
151806
Prove that $A^k = 0 $ iff $A^2 = 0$
34060
Laurent Series of $f(z) = \sin {\frac{1}{z}}$ at $z=0$
125604
Proof that $\mathbb{Z}$ has no zero divisors
30860
Prove that $f(x)=0$ in $[-1,1]$.
121771
Proof $f(x)\equiv 0$
104321
Prove that $1 + \cos\alpha + \cos\beta + \cos\gamma = 0$
20305
Complex roots of $z^3 + \bar{z} = 0$