Problem

Source: Romanian mo 1998

Tags: algebra proposed, algebra



Suppse that n2 and 0<x1<x2<...<xn are integer numbers. We denote that :Sk=A{x1,x2,...,xn}1aAa,k=1,2,...,n. (where A is a non-empty subset). Show that if Sn,Sn1 were positive integer numbers , then k:Sk is a positive integer.