MathDB

N3

Part of 2021 IMO Shortlist

Problems(1)

Prefix sums of divisors are perfect squares

Source: ISL 2021 N3

7/12/2022
Find all positive integers nn with the following property: the kk positive divisors of nn have a permutation (d1,d2,…,dk)(d_1,d_2,\ldots,d_k) such that for i=1,2,…,ki=1,2,\ldots,k, the number d1+d2+⋯+did_1+d_2+\cdots+d_i is a perfect square.
number theoryIMO Shortlist