Question

Please help:
We showed that in any PPT(a,b,c) PPT means Primitive Pythagorean Theorem.
either a or b is even. Use the same sort of assignment to show that either a or b must be a multiple of 3. thanks.

Answer 1

For any Pythagorean Triple, a,b,c, we can write those numbers as
\[ a = k(m^2 - n^2), \ \ \ \ b = k.2mn, \ \ \ \ c = k(m^2 + n^2) \]

Now, notice we factor the expression for a as
\[ a = k(m-n)(m+n) \]

To show that 3 is a divisor of a or b, show that 3 must divide (at least) one of
m, n, m-n, m+n.