Question 60
Let $p$ be a fixed prime number. Juku and Miku play the following game. One of the players chooses a natural number $a$ such that $a \gt 1$ and $a$ is not divisible by $p$, his opponent chooses any natural number $n$ such that $n \gt 1$. Miku wins if the natural number written as $n$ ones in the positional numeral system with radix $a$ is divisible by $p$, otherwise Juku wins. Which player has a winning strategy if:
a. Juku chooses the number $a$, tells it to Miku and then Miku chooses the number $n$;
b. Juku chooses the number $n$, tells it to Miku and then Miku chooses the number $a$?
a. Juku chooses the number $a$, tells it to Miku and then Miku chooses the number $n$;
b. Juku chooses the number $n$, tells it to Miku and then Miku chooses the number $a$?