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Bosnia and Herzegovina EGMO TST 2017 Problem 3

Source: Bosnia and Herzegovina EGMO Team Selection Test 2017

September 19, 2018
Sequencenumber theoryDivisors

Problem Statement

For positive integer nn we define f(n)f(n) as sum of all of its positive integer divisors (including 11 and nn). Find all positive integers cc such that there exists strictly increasing infinite sequence of positive integers n1,n2,n3,...n_1, n_2,n_3,... such that for all i∈Ni \in \mathbb{N} holds f(ni)−ni=cf(n_i)-n_i=c
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