Chapter18An Introduction to Functions

The further one goes into number theory, the more one needs to think about the functions involved as functions, and not just as handy computational shorthand. What properties do these number-theoretic functions (such as \(\phi(n)\)) have? What can we do with them? Most of the remainder of the text deals with such questions. This short chapter introduces some of the questions we will ask through the lens of one function we have done a fair amount with, and then through the eyes of one we have examined in less detail.