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Problem 4 -- Proportional Divisors

Source: 47th Austrian Mathematical Olympiad National Competition Part 1 Problem 4

July 28, 2018
AustriaDivisorsrationumber theory

Problem Statement

Determine all composite positive integers nn with the following property: If 1=d1<d2<⋯<dk=n1 = d_1 < d_2 < \cdots < d_k = n are all the positive divisors of nn, then
(d2−d1):(d3−d2):⋯:(dk−dk−1)=1:2:⋯:(k−1)(d_2 - d_1) : (d_3 - d_2) : \cdots : (d_k - d_{k-1}) = 1:2: \cdots :(k-1)
(Walther Janous)
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