1990 IMO Problems/Problem 5
5. Given an initial integer , two players, and , choose integers , . . . alternately according to the following rules: Knowing , chooses any integer such that . Knowing , chooses any integer such that is a prime raised to a positive integer power. Player wins the game by choosing the number 1990; player wins by choosing the number 1. For which does: (a) have a winning strategy? (b) have a winning strategy? (c) Neither player have a winning strategy?