MathDB
meaningful

Source: Nordic 2019, P1

April 7, 2019
algebranumber theory

Problem Statement

A set of different positive integers is called meaningful if for any finite nonempty subset the corresponding arithmetic and geometric means are both integers. a)a) Does there exist a meaningful set which consists of 20192019 numbers? b)b) Does there exist an infinite meaningful set? Note: The geometric mean of the non-negative numbers a1,a2,⋯ ,a_1, a_2,\cdots, ana_n is defined as a1a2⋯ann.\sqrt[n]{a_1a_2\cdots a_n} .
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