MathDB

5

Part of 1997 Bosnia and Herzegovina Team Selection Test

Problems(1)

Bosnia and Herzegovina TST 1997 Day 2 Problem 2

Source: Bosnia and Herzegovina Team Selection Test 1997

9/20/2018
a)a) Prove that for all positive integers nn exists a set MnM_n of positive integers with exactly nn elements and:
i)i) Arithmetic mean of arbitrary non-empty subset of MnM_n is integer ii)ii) Geometric mean of arbitrary non-empty subset of MnM_n is integer iii)iii) Both arithmetic mean and geometry mean of arbitrary non-empty subset of MnM_n is integer
b)b) Does there exist infinite set MM of positive integers such that arithmetic mean of arbitrary non-empty subset of MM is integer
Setsgeometric meanarithmetic meanalgebranumber theory