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Problem 4 of Finals

Source: IV International Festival of Young Mathematicians Sozopol 2013, Theme for 10-12 grade

January 25, 2020
number theoryalgebraSum

Problem Statement

Let aia_i, i=1,2,...,ni=1,2,...,n be non-negative real numbers and ∑i=1nai=1\sum_{i=1}^na_i =1. Find max⁡S=∑i∣jaiaj\max S=\sum_{i\mid j}a_i a_j .
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