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Differences of divisors form geometric progression

Source: Serbia 2024 MO Problem 1

April 4, 2024
geometric sequencenumber theory

Problem Statement

Find all positive integers nn, such that if their divisors are 1=d1<d2<…<dk=n1=d_1<d_2<\ldots<d_k=n for k≥4k \geq 4, then the numbers d2−d1,d3−d2,…,dk−dk−1d_2-d_1, d_3-d_2, \ldots, d_k-d_{k-1} form a geometric progression in some order.
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