http://www.math.tamu.edu/~map/courses/627-sp08/
(A) Let p be a prime number. For a non-zero rational number x, let ord_p(x) = k, where x = p^k*m/n, for integers m, n both relatively prime to p. We set ord_p(0) = infinity. For x, y rational numebrs, prove the following:
(B) This problem can be done in conjunction with 2.2. Let Z be the integers and Q the rational numbers. Show that the map sending (a,b,c) to (a/c,b/c) from { (a,b,c) in Z^3 | (a,b,c) is a primitive Pythagorean triple } to { (x,y) in Q^2 | x^2 + y^2 = 1 } is a bijection.