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all integers that can occur as the average of a centenary set

Source: Dutch NMO 2022 p2

November 17, 2022
number theory

Problem Statement

A set consisting of at least two distinct positive integers is called centenary if its greatest element is 100100. We will consider the average of all numbers in a centenary set, which we will call the average of the set. For example, the average of the centenary set {1,2,20,100}\{1, 2, 20, 100\} is 1234\frac{123}{4} and the average of the centenary set {74,90,100}\{74, 90, 100\} is 8888. Determine all integers that can occur as the average of a centenary set.
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