2017 OIM Problems/Problem 5
Problem
Given a positive integer 
, all its positive integer divisors are written in a blackboard. Ana and Beto play the following game:
By turns, each one will paint one of those dividers red or blue. They can choose the color they wish in each turn, but they can only paint numbers that have not been painted before. The game ends when all the numbers have been painted. If the product of numbers painted red is a perfect square, or if there are no numbers painted red, Ana wins; Otherwise, Beto wins. If Ana has the first turn, find for each who has a winning strategy.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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