Showing that $e^z=z$ has infinitely many solutions
28148
Are there any simple ways to see that $e^z-z=0$ has infinitely many solutions?
114996
$x+y+z=n$. Finding the number of solutions.
128107
find all $ a \in \mathbb N $ such that $2^a − 1 \equiv 0 \pmod 3$ and $ 4x^2 + 1 \equiv 0 \pmod {\frac{2^a -1}{3}}$ has a solution
103304
Finding the number of solutions to a diophantine equation
148910
Multivariate polynomials have infinitely many zeroes
75957
Prove $x^3+3y^3+9z^3-9xyz=1$ has infinity integers solutions!
151732
Number of solutions of polynomials in a field
95494
Number of solutions of an arithmetic function's equation
89590
The number of solutions of $ax^2+by^2\equiv 1\pmod{p}$ is $ p-\left(\frac{-ab}{p}\right)$
96185
Solutions of $x^2+y^2+z^2 = n$ in $\mathbb{Z}_2$.
6484
Polynomials in one variable with infinitely many roots.
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
7085
Prove that if the equation $x^{2} \equiv a\pmod{pq}$ has any solutions, then it has four solutions.
57191
Show that if $a>e$, the equation $az^n=e^z$ admit $n$ roots in the unit disk - Rouché theorem
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
82571
Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
126018
Show that $ e^{A+B}=e^A e^B$