1. The problem statement, all variables and given/known data Prove that if a right triangle has all sides rational and primitives (co-primes), then one of the smaller side must be even number. 2. Relevant equations For a right triangle (a,b,c) with c is the hypotenuse. $$a^2+b^2=c^2$$ 3. The attempt at a solution In order to create a contradiction, I assume both a and b are odd, so. $$a=2n_1 +1$$ and. $$b=2n_2+1$$ applying Pythagorean theorem, $$a^2+b^2=4(n_1^2+n_2^2-n_1-n_2)+2$$. This only gives me that c must be even but it does not tell me whether it is still rational and co-primes to a and b or not.