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Representation of 1

Source: Singapore Mathematical Olympiad 2006 Problem 2

July 7, 2006
arithmetic sequencealgebra proposedalgebra

Problem Statement

Show that any representation of 1 as the sum of distinct reciprocals of numbers drawn from the arithmetic progression {2,5,8,11,...}\{2,5,8,11,...\} such as given in the following example must have at least eight terms: 1=12+15+18+111+120+141+1110+116401=\frac{1}{2}+\frac{1}{5}+\frac{1}{8}+\frac{1}{11}+\frac{1}{20}+\frac{1}{41}+\frac{1}{110}+\frac{1}{1640}
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