1. Prove that the algorithm is partially correct. To do so, show that as when and are reassigned in each iteration of the loop their greatest common divisor does not change. 2. Show that the loop iterates times. (HINT: prove that decreases by at least of its prior value in each iteration of the loop). 3. Make an argument for full correctness that does not involve explicitly adding a proof of termination.

Why were most movies from the late 1890s until the early 1930s only filmed in black and white? there were only a few people who could afford the technology to produce color motion pictures back then. audiences did not want color motion pictures until later. the film used to make color motion pictures often overheated, which was a safety hazard, so it was generally not allowed. color films had to be hand-colored, frame by frame.