On a particular case of the Dirichlet's theorem and the Midy's property
  We give new characterizations of the Midy's property and using these results we obtain a new proof of a special case of the Dirichlet's theorem about primes in arithmetic progression. 
John H. Castillo and Gilberto Garc\'ia-Pulgar\'in and Juan Miguel   Vel\'asquez-Soto
math.NT