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Divisors on number

Source: All Russian Olympiad 2017,Day1,grade 10,P5

May 3, 2017
number theory

Problem Statement

nn is composite. 1<a1<a2<...<ak<n1<a_1<a_2<...<a_k<n - all divisors of nn. It is known, that a1+1,...,ak+1a_1+1,...,a_k+1 are all divisors for some mm (except 1,m1,m). Find all such nn.
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