Fixed points of the RSA encryption algorithm

In this paper the problem of the number of fixed points for an RSA algorithm is considered. This is an important question from the point of view of any cryptosystem. We have estimated the expected value of this number for randomly chosen RSA parameters. It turned out that it is O(ln2n), and the probability of finding such a point is O(ln2n/n). Thus, these values are really negligible, which had been intuitively expected.