MathDB

4

Part of 2016 CentroAmerican

Problems(1)

Game with coprime integers

Source: Centroamerican 2016, problem 4

6/21/2016
The number "3" is written on a board. Ana and Bernardo take turns, starting with Ana, to play the following game. If the number written on the board is nn, the player in his/her turn must replace it by an integer mm coprime with nn and such that n<m<n2n<m<n^2. The first player that reaches a number greater or equal than 2016 loses. Determine which of the players has a winning strategy and describe it.
gamesnumber theory