Show that the equation $e^z=az^n$ has $n$ solutions in the unit disc centred at the origin counting multiplicity.
57191
Show that if $a>e$, the equation $az^n=e^z$ admit $n$ roots in the unit disk - Rouché theorem
95669
Solutions of $|z| = z^5$ in $\Bbb{C}$?
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
125647
Solutions to the matrix equation $\mathbf{AB-BA=I}$ over general fields
96859
Find the number of zeroes of $p(z)=z^6+z^3+10z^2+4z+3$ inside the annulus $1<|z|<2$
111696
Show $\sin x = bx$ has at least 3 real solutions.
73478
Show that the equation $a_1e^{\alpha_1x} + a_2e^{\alpha_2x} + \cdots + a_ne^{\alpha_nx} = 0$ has at most $n - 1$ real roots.
140009
Show complex solutions exist
145509
Prove the roots of $p(z)+z^n\bar{p}(\frac{1}{z})$ lie on the unit circle
39993
Count the number of positive solutions for a linear diophantine equation
99739
The diophantine equation $x^2+y^2=3z^2$
62036
Finding the number of non-negative integral solutions of $x + y + z = 10$
156468
Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
146491
Number of solutions of $x_1+x_2+\dots+x_k=n$ with $x_i\le r$
22840
The sum of the first $n$ squares is a square: a system of two Pell-type-equations
35066
Nature and number of solutions to $xy=x+y$
124300
$\lambda-z-e^{-z}=0$ has one solution in the right half plane