RSA system

1. In an RSA system, the public key of a given user is e = 31, n = 3599. What is the private key of this user?

2. Suppose we have a set of blocks encoded with the RSA algorithm and we don’t have the private key. Assume n = pq, e is the public key. Suppose also someone tells us they know one of the plaintext blocks has a common factor with n. Does this help us in any way?

3. Show how RSA can be represented by matrices M1, M2, and M3 of Problem