I have been struggling with this problem for quite some time now but i haven't been able to find a solution yet. My first approach was to try and make an Euler's Brick type form but that didn't really work. Then i generalised it for two such numbers to get {(x,y)}={(n²-2nm+2m²,2nm-2m²)} where n>2m.
After solving some more and making some equations I ended up with equations which represented stuff like
a-b+b+c=a+c
Just in complicated perfect square forms. And then I got stuck. Can anyone please help me solve this problem?