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Consecutive divisors two apart

Source: IOM 2018 #4, Ivan Mitrofanov

September 6, 2018
number theoryIOM

Problem Statement

Let 1=d0<d1<⋯<dm=4k1 = d_0 < d_1 < \dots < d_m = 4k be all positive divisors of 4k4k, where kk is a positive integer. Prove that there exists i∈{1,…,m}i \in \{1, \dots, m\} such that di−di−1=2d_i - d_{i-1} = 2.
Ivan Mitrofanov
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