Let p and q be primes

Let p and q be primes. Let E and D be an encryptor and decryptor that work for
the RSA encoding process with N = pq.
Now consider RSA encoding with N = pq, and encryptor E
2
. Prove that D2
is a
decryptor for this encryptor.
Note: This question is describing the following situation: suppose you “doubly”
encode the message M by encoding once using E (obtaining ME) and then again
using E (obtaining
ME
E
). You are asked to show that by using D2 you can decode
the doubly encrypted message in one step, instead of doing so in two steps. In other
words, “doubly” encoding your message adds no additional security.