The Number of the Modulo n Roots of the Polynomial xv − xu and the RSA

RSA is one of the oldest and until now one of the most widely used public key cryp- tographic systems, which is based on the modular raising to power. In this article it is pointed out that most of the essential properties of the RSA can be read out from the number of the modulo n roots of the polynomial mentioned in the title of this article. The results explain almost all of the properties taken into account at the choice of the parameters of the RSA. By the help of the polynomial it is pointed out how the modulus and the exponent must be chosen so that the modular raising to power realizes a secure cryptosystem. The article investigates also the role of the choice of the parameters related to the success of the cycling attack. The article conveys a unified point of view for the examination of a lot of the number theoretic problems arising with respect to the RSA.