Here is a very, very fun game. We start with two distinct, positive integers written on a blackboard. Call them r and y. You and I now take turns. (I'll let you decide who goes first.) On each player's turn, he or she must write a new positive integer on the board that is a common divisor of two numbers that are already there. If a player can not play, then he or she loses. For example, suppose that 12 and 15 are on the board initially. Your first play can be 3 or 1. Then I play 3 or 1, whichever one you did not play. Then you can not play, so you lose. (a) [6 pts] Show that every number on the board at the end of the game is either x, y, or a positive divisor of ged(x, y). (b) [6 pts] Show that every positive divisor of gcd(x, y) is on the board at the end of the game. (c) [6 pts] Describe a strategy that lets you win this game every time.