Proving that there exists a solution to the quadratic equation
96185
Solutions of $x^2+y^2+z^2 = n$ in $\mathbb{Z}_2$.
141529
Proving existence of a minimum
110297
Problem related to quadratic equations
140009
Show complex solutions exist
58311
How to find the solution of a quadratic equation with complex coefficients?
14517
Existence of solutions of the equation with a limit.
131120
Proving an integral equation.
17786
Existence of Consecutive Quadratic residues
63689
proving roots of equation $x^2+x+4f=0$ are real.
42713
Solutions to the equation $ze^{a-z}=1$
39170
Existence of square root
115583
prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
144851
For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
7085
Prove that if the equation $x^{2} \equiv a\pmod{pq}$ has any solutions, then it has four solutions.
138186
Proving the given quadratic form is chi-squared $k$