Problem

Source: Morocco TST 2010, problem 3

Tags: number theory, prime numbers



Any rational number admits a non-decimal representation unlimited decimal expansion. This development has the particularity of being periodic. Examples: $\frac{1}{7} = 0.142857142857…$ has a period $6$ while $\frac{1}{11}=0.0909090909 …$ $2$ periodic. What are the reciprocals of the prime integers with a period less than or equal to five?