Problem

Source: SRMC 2002

Tags: number theory unsolved, number theory



Observe that the fraction $ \frac{1}{7}=0,142857$ is a pure periodical decimal with period $ 6=7-1$,and in one period one has $ 142+857=999$.For $ n=1,2,\dots$ find a sufficient and necessary condition that the fraction $ \frac{1}{2n+1}$ has the same properties as above and find two such fractions other than $ \frac{1}{7}$.