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Number of ideal subsets, n+p and n+q belong to S

Source: IMO Shortlist 2000, C6

August 10, 2008
modular arithmeticnumber theorycombinatoricsAdditive Number TheoryAdditive combinatoricsIMO ShortlistFrobenius

Problem Statement

Let p p and q q be relatively prime positive integers. A subset S S of {0,1,2,…} \{0, 1, 2, \ldots \} is called ideal if 0∈S 0 \in S and for each element n∈S, n \in S, the integers n \plus{} p and n \plus{} q belong to S. S. Determine the number of ideal subsets of {0,1,2,…}. \{0, 1, 2, \ldots \}.
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