3.6-3.7

1. So if n is a Carmichael number and (a,n)=1 (which means a does not share what I assume is a small number of prime factors), a^phi(n)=1 (mod n) and the Euler-Fermat theorem fails?

2. I am fascinated by logarithms, probably because I don't understand them beyond basic application. I think they are analytic which boggles my mind: how numbers can contain in themselves and their algebraic relationships so much information. The discrete logarithm is also interesting because I can see how it would be useful but I have no idea how to go about finding it.