Here's the game: the first player picks an integer n > 1 , then the second player subtracts a proper divisor d < n of that number, telling the first player the difference n - d , then the first player subtracts a proper divisor of that new number, etc. The player who announces a difference of 1 is the winner. Does either player have a winning strategy? If not explain why not; if so, which player is it, does it depend on n, and what's the strategy?

note: A positive proper divisor is a positive divisor of a number n, excluding n itself. For example, 1, 2, and 3 are positive proper divisors of 6, but 6 itself is not.

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