MathDB

Number theory or function ?

Source: IMO ShortList 2004, algebra problem 3

March 18, 2005

functionnumber theorycontinued fractionalgebrafunctional equationIMO Shortlist

Problem Statement

Does there exist a function

s\colon \mathbb{Q} \rightarrow \{-1,1\}

such that if

x

and

y

are distinct rational numbers satisfying

{xy=1}

{x+y\in \{0,1\}}

, then

{s(x)s(y)=-1}

? Justify your answer.
Proposed by Dan Brown, Canada