I need to teach a course in elementary number theory next academic year. What topics should be included on a first course in this area? What is best order of doing things? The students have a minimum background in proof but this is a second year undergraduate module. I am looking for applications which will motivate the student in this subject. Are there good resources on elementary number theory?
The best thing would be to follow David M. Burton's book 'Elementary Number Theory'.
You could do much worse than to use Underwood Dudley, Elementary Number Theory; it’s $35$ years old, but it’s very readable, it has all of the traditional topics, and it’s available in an inexpensive Dover paperback edition and an even more inexpensive Kindle edition.