MathDB

rational and irrational

Source: APMO 2005 Problem 1

March 23, 2005

Problem Statement

Prove that for every irrational real number

a

, there are irrational real numbers

b

and

b'

so that

a+b

and

ab'

are both rational while

ab

and

a+b'

are both irrational.

Back to Problems View on AoPS