Aliquot Game

Aliquot part is another name for a proper divisor, i.e. any divisor of a given number other than the number itself. A prime number has only one aliquot part - the number 1. 1, 2, 3, 4, 6 are all aliquot parts of 12. The number 1 does not have aliquot parts. In the Aliquot game, players take turns subtracting an aliquot part of the number left by their opponent. The winner is the last player able to perform such a subtraction. The loser is the player left with a number that has no aliquot parts - 1. Thus the objective of the game is to leave your opponent without a move. What is the winning strategy?


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aliquot game


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