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Source: Kyiv City MO 2024 Round 1, Problem 8.5

January 28, 2024
number theoryDivisors

Problem Statement

Find the smallest positive integer nn that has at least 77 positive divisors 1=d1<d2<…<dk=n1 = d_1 < d_2 < \ldots < d_k = n, k≥7k \geq 7, and for which the following equalities hold:
d7=2d5+1 and d7=3d4−1d_7 = 2d_5 + 1\text{ and }d_7 = 3d_4 - 1
Proposed by Mykyta Kharin
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