Suppse that n≥2 and 0<x1<x2<...<xn are integer numbers. We denote that :Sk=∑A⊂{x1,x2,...,xn}1∏a∈Aa,k=1,2,...,n. (where A is a non-empty subset). Show that if Sn,Sn−1 were positive integer numbers , then ∀k:Sk is a positive integer.
Source: Romanian mo 1998
Tags: algebra proposed, algebra
Suppse that n≥2 and 0<x1<x2<...<xn are integer numbers. We denote that :Sk=∑A⊂{x1,x2,...,xn}1∏a∈Aa,k=1,2,...,n. (where A is a non-empty subset). Show that if Sn,Sn−1 were positive integer numbers , then ∀k:Sk is a positive integer.