Question 171
Observe that the fraction $1/7 = 0.\overline{142857}$ 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 $1/(2n+1)$ has the same properties as above and find two such fractions other than $1/7$.