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A number theory in China Second Round(B)

Source: 2019 China Second Round(B) P2

September 8, 2019
number theory

Problem Statement

Find all the positive integers nn such that: (1)(1) nn has at least 44 positive divisors. (2)(2) if all positive divisors of nn are d1,d2,⋯ ,dk,d_1,d_2,\cdots ,d_k, then d2−d1,d3−d2,⋯ ,dk−dk−1d_2-d_1,d_3-d_2,\cdots ,d_k-d_{k-1} form a geometric sequence.
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