In a Primitive Pythagorean Triple (PPT) the set $(a, b, c)$ has GCD of 1.
I have read in the wiki page that every other Pythagorean triple can be obtained by multiplying k to this set $(ka, kb, kc)$ where $k$ is some positive integer.
I was wondering if the above statement is true then it's not possible for only 2 values in any Pythagorean triple to have a common factor greater than 1. Since the common factor will be forced to divide even the third value.
If I am not wrong in asking the question taking this equation
$a^2 + b^2 = c^2$
how to prove the above fact?