Hello all, I'm practicing proofs and I'm stuck. Here it is: Prove that there are infinitely many solutions in positive integers x, y, and z to the equation x^2 + y^2 = z^2. Evidently I'm supposed to start by setting x, y, and z like this: x = m^2 - n^2 y = 2mn z = m^2 + n^2 So then we have: (m^2 - n^2)^2 + (2mn)^2 = (m^2 + n^2)^2 m^4 + n ^4 - 2(mn)^2 + 4(mn)^2 = m ^4 + n^4 +2(mn)^2 m ^4 + n^4 +2(mn)^2 = m ^4 + n^4 +2(mn)^2 Now I'm sort of at a standstill. I understand that I can plug any integer into m and n and x^2 + y^2 = z^2 will be true, but I'm not sure how to prove it. Also, another way to show the proof would be to let x be: x = 3m y = 4m z = 5m Since any number can be plugged into m then there are infinite solutions. However, I would like to understand how to derive the proof from my first method. I'm really trying to understand this stuff so any help would be appreciated.