MathDB

Azambuja writes a rational number

q

on a blackboard. One operation is to delete

q

and replace it by

q+1

; or by

q-1

; or by

\frac{q-1}{2q-1}

q \neq \frac{1}{2}

. The final goal of Azambuja is to write the number

\frac{1}{2018}

after performing a finite number of operations. a) Show that if the initial number written is

0

, then Azambuja cannot reach his goal. b) Find all initial numbers for which Azambuja can achieve his goal.

Problem Statement