Two people play a game, lets call them A and B. There are $n$ stones on a table and players start to remove them. They can remove $p-1$ stones at once where $p$ is a prime number. Whoever takes the last stone, wins. Show that if player A starts then player B has a winning strategy for infinite number of $n$.
My thoughts so far:
It seems that whoever can take stones such that 3 stones remain will win. I haven't figured out when it is impossible for player A to do so. Player B needs to avoid a position where there are $p+2$ stones remaining. Any ideas on how to go about this?