11
votes
1answer
346 views

Symmetric functions on three parameters being perfect squares

Is it possible for $x+y+z, xy+yz+zx$, and $xyz$ to be perfect squares at the same time for positive integer values of $x,y,z$?
3
votes
0answers
318 views

The surface $ x^2 y^2 + 1 = (x^2 + y^2) z^2 $

Hi, I'm trying to find all rational points on the surface of the title, in connection with the Euler Brick (AKA Rational Box) problem. This surface is equivalent to $ x^2 z^2 - 1 = (x^2 - z^2) y^2 $, ...