MathDB

Gcd

Source: Indian RMO 1994 problem 5

October 25, 2005

number theorygreatest common divisor

Problem Statement

Let

A

be a set of

16

positive integers with the property that the product of any two distinct members of

A

will not exceed 1994. Show that there are numbers

a

and

b

in the set

A

such that the gcd of

a

and

b

is greater than 1.