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difference between odd pos. divisors and even pos. divisors inequality

Source: 2017 Romania JBMO TST 4.2 - Kurschak Competition, 1999

June 27, 2020
inequalitiesnumber theoryDivisorsDifference

Problem Statement

Let nn be a positive integer. For each of the numbers 1,2,..,n1, 2,.., n we compute the difference between the number of its odd positive divisors and its even positive divisors. Prove that the sum of these differences is at least 00 and at most nn.
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