the information given to me is :
a triple (a, b,c ) of natural numbers is called a Pythagorean triple iFF
a^2 + b^2 = c^2. A Pythagorean triple (a ,b ,c ) is called primitive IFF a, b, and c have no common factor.
In the following, let u,v be elements of N such that u.v and gcd(u,v) =1, and define a= u^2 -v^2 = 2uv and c= u^2 +v^2
I am asked 1: Is ( a,b ,c ) a Pythagorean triple
2. If both u and v are odd, then (a,b,c)is not primitive