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TOT 427 1994 Autumn A J4 subsequence from 1,1/2,1/3, ...

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June 12, 2024
algebraSequence

Problem Statement

From the sequence 1,12,13,...1,\frac12, \frac13, ... can one choose
(a) a subsequence of 100100 different numbers, (b) an infinite subsequence
such that each number (beginning from the third) is equal to the difference between the two preceding numbers (ak=ak−2−ak−1a_k=a_{k-2}-a_{k-1})?
(SI Tokarev)
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