Prove that if a right triangle has all sides rational and primitives (co-primes), then one of the smaller side must be even number.
For a right triangle (a,b,c) with c is the hypotenuse.
The Attempt at a Solution
In order to create a contradiction, I assume both a and b are odd, so.
applying Pythagorean theorem,
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.