Sum and product of purely periodic decimal fractions
Source: All-Russian Olympiad 2006 finals, problem 11.2
May 6, 2006
number theory proposednumber theory
Problem Statement
The sum and the product of two purely periodic decimal fractions and are purely periodic decimal fractions of period length . Show that the lengths of the periods of the fractions and are not greater than .
Note. A purely periodic decimal fraction is a periodic decimal fraction without a non-periodic starting part.