Proving $a^2 + b^2 = c^2 \implies (ma)^2 + (mb)^2 = (mb)^2$

Question

Hi I am new to this community and not too sure how to write questions up to par.

How can I prove $$a^2 + b^2 = c^2 \implies (ma)^2 + (mb)^2 = (mb)^2, $$

for all $a,b,c,m$ positive natural numbers.

Answer 1

Multiply the equation by $m^2$ and use the general rule $x^2y^2 = (xy)^2$.