Question 83
For a positive integer $n$, two players $A$ and $B$ play the following game: Given a pile of $s$ stones, the players take turns alternatively with $A$ going first. On each turn the player is allowed to take either one stone, or a prime number of stones, or a multiple of $n$ stones. The winner is the one who takes the last stone. Assuming both $A$ and $B$ play perfectly, for how many values of $s$ can player $A$ not win?