Do there exist 2009 distinct positive integers
Source: Hungary-Israel Binational Olympiad 2009, Problem 6
August 17, 2009
inductionnumber theory unsolvednumber theory
Problem Statement
(a) Do there exist 2009 distinct positive integers such that their sum is divisible by each of the given numbers?
(b) Do there exist 2009 distinct positive integers such that their sum is divisible by the sum of any two of the given numbers?