MathDB

{P_{x\in A} x} / |A|} and P_{x\in B} x} / |B| are two relatively prime compos

Source: Indian Postal Coaching 2009 set 2 p1

May 26, 2020

number theorySubsetscombinatorics

Problem Statement

Let

n \ge 1

be an integer. Prove that there exists a set

S

n

positive integers with the following property: if

A

and

B

are any two distinct non-empty subsets of

S

, then the averages

\frac{P_{x\in A} x}{|A|}

and

\frac{P_{x\in B} x}{|B|}

are two relatively prime composite integers.