Lior posted a list of Pythagorean triangles to a different thread, and mentioned that there are infinitely many such triangles. Since many of the ones on his list were similar to others, I am sure that he did not use the following cute algorithm.
  • Choose an odd and an even integer (u, v) with no common factor and u > v.
    For example: (3, 2) (24, 5) (49, 36), but not (7, 3) or (33, 6).
  • z = u^2 + v^2
  • y = u^2 - v^2
  • x = 2*u*v
x^2 + y^2 = z^2, and x, y, z will have no common factor.