How to prove that $x^2+y^2+z^2 = 2xyz$ has no solutions over the positive integers?
72023
Integer solutions of the equation $x^2+y^2+z^2 = 2xyz$
41364
How to prove that $x^y - y^x = x + y$ has only one solution in positive integers?
55248
Positive integral solutions of $3^x+4^y=5^z$
123159
Solutions of the diophantine equation $x+y+z=xyz$?
147442
Quadratic Diophantine Equation $x^2 + axy + y^2 = z^2$
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
50760
Solutions to $y^2 = x^3 + k$?
117352
Show $x^n+ax+b=0$ has most two solutions
105336
What are the solutions to $z^4+1=0$?
77763
Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers
41073
Prove $ax^2+bx+c=0$ has no rational roots if $a,b,c$ are odd
155743
Why does the equation $x^2\equiv2 \pmod 5$ have no solutions?
94700
Integer solutions for $x^3+2=y^2$?
70662
How many non-negative integer solutions does the equation $3x + y + z = 24$ have?
143281
How to solve $z^2-(1-3i)z-2i-2=0$
79544
Prove $x^3 + 3 =4y(y+1)$ has no integer solutions
13120
Find all integer solutions to $x^2+y^2+z^2=2xyz$