How do I prove that $(2mn, m^2 - n^2, m^2 + n^2)$ is true for $m>n>0$?
Since $m^2 + n^2$ is the hypotenuse, I applied the Pythagoren theorem: $(2mn)^2 + (m^2 - n^2)^2 = (m^2 +n^2)^2$ and simplified it so that I would get $(m^2 + n^2)^2 = (m^2 + n^2)^2$ but I wasn't able to prove anything. How do I continue from here?
Thanks!