In calculus, you learn to solve (or at least find approximate solutions to) equations of the form . Solving for in terms of incolves using the logarithm to base .
We want to do something analogous here. One difference here is that, because the integers are discrete, there are no approximate solutions!
For example, the order of modulo is since .
One way to think about the material in this section is it is a study of properties of the order function. The order of an integer is not ``easy'' to find in the sense that if is a large integer then there is no known ``efficient'' algorithm for determining [BS].