<s>[INST] How to prove this Pythagorean Triple? 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!
 [/INST] Realizing that I made a silly mistake, I reevaluated the equation and:
Given the Pythagorean Triple $(2mn, m^2-n^2,m^2+n^2)$ and $m>n>0$, we can apply the Pythagorean theorem to see if they are equal:
$(2mn)^2+(m^2-n^2)^2 = (m^2+n^2)^2$ 
$4m^2n^2 + (m^4-2m^2n^2+n^4) = (m^2+n^2)^2$
$m^4+2m^2n^2+n^4=(m^2+n^2)^2$
$(m^2+n^2)^2 = (m^2 + n^2)^2$
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