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TOT 019 1982 Spring J5 S5 arithmetic progression in 1,1/2,1/3,1/4,...

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August 17, 2019
arithmetic sequence

Problem Statement

Consider the sequence 1,12,13,14,...1, \frac12, \frac13, \frac14 ,... Does there exist an arithmetic progression composed of terms of this sequence (a) of length 55, (b) of length greater than 55 (if so, what possible length)?
(G Galperin, Moscow)