Why $x^2+y^2=3z^2$ (which $z$ is not zero) has only $(0,0,0)=(x,y,z)$ as an answer?
111467
find all natural solution that satisfy $x^2+y^2 = 3z^2$
10068
$f(x,y)= e^{-\frac{1}{x^2+y^2}}$ when $(x,y)\neq (0,0)$ and $f(0,0)=0$.
32771
The equation $X^{n} + Y^{n} = Z^{n}$ , where $ n \geq 3$ is a natural number, has no solutions at all where $X,Y,Z$ are intergers.
122737
How to understand why $x^0 = 1$, where $x$ is any real number?
34393
Variation of Pythagorean triplets: $x^2+y^2 = z^3$
14150
Zero to the zero power – is $0^0=1$?
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
39135
Representation of integers by ternary quadratic form $x^2+y^2-z^2$
29151
Equation with Vieta Jumping: $(x+y+z)^2=nxyz$.
47809
If $x,y\in\mathbb Z$, solve $x^2+xy+y^2=x^2y^2$.
38160
Number of roots of $z^4+z^3+4z^2+2z+3=0$ in each quadrants
133680
On the equation $3x^3 + 4y^3 + 5z^3 = 0$
145152
How to prove that $\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}$ holds for any $(x,y,z)\in[1,2]^3$
24980
What is the order when doing $x^{y^z}$ and why?
147442
Quadratic Diophantine Equation $x^2 + axy + y^2 = z^2$
32760
Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?
114996
$x+y+z=n$. Finding the number of solutions.