MathDB
The longest representation - IMO LongList 1992 ROM3

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September 2, 2010
algorithmalgebraAdditive Number TheoryAdditive combinatoricsIMO ShortlistIMO Longlist

Problem Statement

For any positive integer nn consider all representations n=a1+⋯+akn = a_1 + \cdots+ a_k, where a1>a2>⋯>ak>0a_1 > a_2 > \cdots > a_k > 0 are integers such that for all i∈{1,2,⋯ ,k−1}i \in \{1, 2, \cdots , k - 1\}, the number aia_i is divisible by ai+1a_{i+1}. Find the longest such representation of the number 1992.1992.
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