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14

Part of 2002 Iran MO (3rd Round)

Problems(1)

Eventually linear

Source: Iranian National Olympiad (3rd Round) 2002

10/2/2006
A subset SS of N\mathbb N is eventually linear iff there are k,N∈Nk,N\in\mathbb N that for n>N,n∈S⟺k∣nn>N,n\in S\Longleftrightarrow k|n. Let SS be a subset of N\mathbb N that is closed under addition. Prove that SS is eventually linear.
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