MathDB
Integer average set

Source: Mexico National Olympiad 2017, Problem 2

November 6, 2017
number theoryAverage

Problem Statement

A set of nn positive integers is said to be balanced if for each integer kk with 1≤k≤n1 \leq k \leq n, the average of any kk numbers in the set is an integer. Find the maximum possible sum of the elements of a balanced set, all of whose elements are less than or equal to 20172017.
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