I am trying to solve this diophantine equation: $x^2 + yx + y^2 = z^2$
In other words, I am trying to find integers $x$ and $y$ such that $x^2 + yx + y^2$ is a perfect square.
So far, the only methods to solve quadratic diophantine equations I am familiar with are Pythagorean triples and Pell equations. The $yx$ term has a coefficient of one, so I can't complete the square to reduce it to a Pell equation somehow, and I am wondering if there are other methods to solve this kind of equation.
Some insight would be highly appreciated.