Show that the equation $x^2+y^2+z^2=x^2y^2$ has no integer solution,except $x=y=z=0$
88760
Find the integral solutions to $ x^2+y^2+z^2=x^2y^2$
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
50182
Prove the Mordell's equation $x^2+41=y^3$ has no integer solutions
15753
Solve the following equation in positive integers $x$ and $y$
96185
Solutions of $x^2+y^2+z^2 = n$ in $\mathbb{Z}_2$.
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
20834
Integer solutions to $c=a^2-b^2$
145287
Solve for integers $x, y, z$ such that $x + y = 1 - z$ and $x^3 + y^3 = 1 - z^2$.
150085
Solutions to the diophantine equation: $2a^2 + 2b^2- c^2- d^2 = 0$
55206
Prove that the equation $x^4+(2k^2)x^2+2k^4$ is not a perfect square
10548
The equation $-1 = x^2 + y^2$ in finite fields
66256
Find all solutions of the equality $y^2=x^3+23$ for integers $x,y$
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.
8276
How do I get my equation to have the form $(x-a)^2 + (y-b)^2 + (z-c)^2-d = 0$?
53503
Solving the diophantine equation $y^{2}=x^{3}-2$
7622
$AB-BA=I$ having no solutions