MathDB

x is rational implies y is rational

Source: IMO Shortlist 2006, N2, VAIMO 2007, Problem 6

June 28, 2007

number theoryrationaldecimal representationIMO Shortlist

Problem Statement

For

x \in (0, 1)

let

y \in (0, 1)

be the number whose

n

-th digit after the decimal point is the

2^{n}

-th digit after the decimal point of

x

. Show that if

x

is rational then so is

y

.
Proposed by J.P. Grossman, Canada