IMO Hk TST

Number theory Difficulty 8.2 Shortlist Prove it Hong Kong

Find all positive integers $n$ with the following property: the $k$ positive divisors of $n$ have a permutation $(d_1, d_2, \dots, d_k)$ such that for every $i = 1, 2, \dots, k$ , the number $d_1 + d_2 + \dots + d_i$ is a perfect square.

Solution

2. (IMO Shortlist 2021 N3) See the official solution.

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