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 $\{0, 1, 2, \ldots \}.$
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