Let and be relatively prime positive integers. A subset of is called ideal if and for each element the integers and belong to Determine the number of ideal subsets of
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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 $\{0, 1, 2, \ldots \}.$
Izvor: Međunarodna matematička olimpijada, shortlist 2000
Školjka 
and 
be relatively prime positive integers. A subset 
of 
is called ideal if 
and for each element 
the integers 
and 
belong to 
Determine the number of ideal subsets of 