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Bundeswettbewerb Mathematik 1977 Problem 1.1

Source: Bundeswettbewerb Mathematik 1977 Round 1

October 10, 2022
Integersalgebranumber theorySumdivisible

Problem Statement

Among 20002000 distinct positive integers, there are equally many even and odd ones. The sum of the numbers is less than 3000000.3000000. Show that at least one of the numbers is divisible by 3.3.