6. (10) (Problem 8.12, textbook) Here is a game you can analyze with number theory and always beat me. We start with two distinct, positive integers written on a blackboard. Call them a and b. Now we take turns. (I'll let you decide who goes first.) On each turn, the player must write a new positive integer on the board that is the difference of two numbers that are already there. If a player cannot play, then they lose. For example, suppose that 12 and 15 are on the board initially. Your first play must be 3, which is 15- 12. Then I might play 9, which is 12-3. Then you might play 6, which is 15- 9. Then I can't play, so I lose. (a) Show that every number on the board at the end of the game is a multiple of ged(a, b). (b) Show that every positive multiple of ged(a, b) up to mar(a, b) is on the board at the end of the game (c) Describe a strategy that lets you win this game every time