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Can 2001 be Obtained?

Source: ToT - 2001 Spring Junior O-Level #1

August 17, 2011
inductionnumber theory unsolvednumber theory

Problem Statement

The natural number nn can be replaced by abab if a+b=na + b = n, where aa and bb are natural numbers. Can the number 20012001 be obtained from 2222 after a sequence of such replacements?
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