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List of Factors

Source: 2022 Mexican Mathematics Olympiad P5

November 8, 2022
number theory

Problem Statement

Let n>1n>1 be a positive integer and d1<d2<⋯<dmd_1<d_2<\dots<d_m be its mm positive divisors, including 11 and nn. Lalo writes the following 2m2m numbers on a board: d1,d2…,dm,d1+d2,d2+d3,…,dm−1+dm,Nd_1,d_2\dots, d_m,d_1+d_2,d_2+d_3,\dots,d_{m-1}+d_m,N where NN is a positive integer. Afterwards, Lalo erases any number that is repeated (for example, if a number appears twice, he erases one of them). Finally, Lalo realizes that the numbers left on the board are exactly all the divisors of NN. Find all possible values that nn can take.
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