Right triangle generator

Detective Harry Thomson found on the Internet a generator for the side lengths of right triangles. According to it: a = 2xy, b = x² − y², c = x² + y², where x and y are natural numbers and x > y. Is it a working generator?

Result

q=

Yes

No

Step-by-step explanation:

$$\begin{gathered} a=2xy \\ b=x^2-y^2 \\ c=x^2+y^2 \\ {c}^2=a^2+b^2 \\ (x^2+y^2{)}^2=(2xy{)}^2+(x^2-y^2{)}^2 \\ {x}^4+2\cdot x^2{y}^2+y^4=4x^2{y}^2+x^4-2x^2{y}^2+y^4 \\ 2\cdot x^2{y}^2=4x^2{y}^2-2x^2{y}^2 \\ 2\cdot x^2{y}^2=2x^2{y}^2 \\ 1 \\ q=1 \end{gathered}$$

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