MathDB

Let

n\ge 2

be an integer. Ariane and Bérénice play a game on the number of the residue classes modulo

n

. At the beginning there is the residue class

1

on each piece of paper. It is the turn of the player whose turn it is to replace the current residue class

x

with either

x + 1

or by

2x

. The two players take turns, with Ariane starting. Ariane wins if the residue class

0

is reached during the game. Bérénice wins if she can prevent that permanently. Depending on

n

, determine which of the two has a winning strategy.

Problem Statement