MathDB

Ineq with the number of elements in the sets

Source: Pre-VMO 2012 - Problem 2

November 27, 2011

combinatorics proposedcombinatorics

Problem Statement

Let

A

be a set of finite distinct positive real numbers. Two other sets

B

C

are defined by:

B = \left\{ {\frac{x}{y};x,y \in A} \right\},\; \; \; C = \left\{ {xy;x,y \in A} \right\}

Prove that

\left| A \right|.\left| B \right| \le {\left| C \right|^2}