## Problem of the Week 1235## A Prime Multiplication GameAlice and Bob play a game. The target is an integer N at least 2. The state of the game, M, is an integer that starts out being 1. Players alternate moves, with Alice going first. At each move, a player multiplies M by a prime number that divides N. A player wins by making M equal to N. If M ever exceeds N, the game is a draw. For which values of N does Alice have a winning strategy? For which values of N does Bob have a winning strategy?
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16 March 2017