IMO 2006 Shortlist N2

For x ∈ (0,1) let y ∈ (0,1) be the number whose nth digit after the decimal point is the (2n )th digit after the decimal...

imomathematicsolympiadshortlistnumber-theory

IMO 2006 Shortlist N2

Category: Number Theory

Problem

For x ∈ (0,1) let y ∈ (0,1) be the number whose nth digit after the decimal point is the (2n )th digit after the decimal point of x. Show that if x is rational then so is y. (Canada)