In many of the basic courses in Number Theory, Finite Mathematics and Cryptography we come across the so-called arithmetic functions such as ϕn), σ(n), τ(n), μ(n), etc, whose domain is the set of natural numbers. These functions are well known and evaluated through the prime factor decomposition of n. It is less well known that these functions possess inverses (with respect to Dirichlet multiplication) which have interesting properties and applications.
Introduction to finite mathematics, by J. G. Kemeny, J. L. Snell, G. L. Thompson. Prentice-Hall Inc., Englewood Cliffs, N. J., Second edition, 1966. xiv + 465 pages. $8.95.
