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d_i are all the proper divisors of n, d_i+1 are all the proper divisors of m

Source: Danube 2018 junior p1

July 22, 2019
number theoryDivisorsComposite

Problem Statement

Find all the pairs (n,m)(n, m) of positive integers which fulfil simultaneously the conditions: i) the number nn is composite; ii) if the numbers d1,d2,...,dk,k∈N∗d_1, d_2, ..., d_k, k \in N^* are all the proper divisors of nn, then the numbers d1+1,d2+1,...,dk+1d_1 + 1, d_2 + 1, . . . , d_k + 1 are all the proper divisors of mm.
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