No positive integer greater than 1 divides all the elements
Source: IMO Longlist 1989, Problem 82
September 18, 2008
group theoryabstract algebranumber theory unsolvednumber theory
Problem Statement
Let be a set of positive integers such that no positive integer greater than 1 divides all the elements of Prove that any sufficiently large positive integer can be written as a sum of elements of (Elements may occur several times in the sum.)