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d_k-eja Vu

Source: 2024 USAMO Problem 1

March 20, 2024
USAMOnumber theory

Problem Statement

Find all integers n≥3n \geq 3 such that the following property holds: if we list the divisors of n!n! in increasing order as 1=d1<d2<⋯<dk=n!1 = d_1 < d_2 < \dots < d_k = n!, then we have d2−d1≤d3−d2≤⋯≤dk−dk−1. d_2 - d_1 \leq d_3 - d_2 \leq \dots \leq d_k - d_{k-1}.
Proposed by Luke Robitaille.
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