Prove that there are infinitely many solutions in positive integers x, y, and z to the equation x2 +y2 = z2. [Hint: Let x = m2 – n2, y = 2mn, and z = m2 + n2, where m and n are integers.]

Step 1:

Here the objective is to prove that there are infinitely many solutions in positive integers x,y,z to the equation