Question 6
C6 (FRA). Let $p$ and $q$ be relatively prime positive integers. A subset $S$ of $\{0,1,2,\ldots\}$ is called ideal if $0\in S$ and for each element $n\in S$, the integers $n+p$ and $n+q$ belong to $S$. Determine the number of ideal subsets of $\{0,1,2,\ldots\}$.