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Smallest Positive Integer

Source: BdMO 2023 Higher Secondary National P3

February 12, 2023
functionnumber theory

Problem Statement

For any positive integer nn, define f(n)f(n) to be the smallest positive integer that does not divide nn. For example, f(1)=2f(1)=2, f(6)=4f(6)=4. Prove that for any positive integer nn, either f(f(n))f(f(n)) or f(f(f(n)))f(f(f(n))) must be equal to 22.
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