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Sequence and divisibility

Source: Tournament of Towns,Spring 2002, Junior A Level, P6

May 13, 2014

inductioninequalitiesnumber theory proposednumber theory

Problem Statement

In an infinite increasing sequence of positive integers, every term from the

2002^{\text{th}}

term divides the sum of all preceding terms. Prove that every term starting from some term is equal to the sum of all preceding terms.