I have come up with an equation recently from a project that I'm doing. it's like the Pythagorean theorem except it's $2c^2$ rather than the familiar $c^2$, then I decided that I wanted a list of all the equations that could give me all "Pythagorean Triples", but I don't know where to start (except guess and check).
If anyone is willing, I would like some help on creating this list. I have already found a few, but I can't see any pattern that links them together besides c looks like its always a multiple of a prime number that is one more than a multiple of four.
- $x^2+x^2 = 2x^2$