Question 48
Let $p$, $q$ be positive integers. To start off, we write the integer $1$ on a blackboard. Then, we repeat the following operation:
Operation: Choose $p$ or $q$ and replace the number written on the blackboard by the number obtained by adding the chosen number to it.
Find a condition on $p$, $q$ which guarantees that the operation can be repeated indefinitely without writing any multiples of $p$ or $q$.
Operation: Choose $p$ or $q$ and replace the number written on the blackboard by the number obtained by adding the chosen number to it.
Find a condition on $p$, $q$ which guarantees that the operation can be repeated indefinitely without writing any multiples of $p$ or $q$.