I'm an undergraduate student and I would like to learn olympiad level-number theory. For what I've read, Number theory: Structures, Examples and Problems is a great book, however, I'm not sure it is a good book to learn the subject. I've skimmed through the first pages and it seems that some of the problems require one to have a little knowledge of number theory, but I'm not completely sure about it. I would like a book that gives you strong background and also I would like that the book doesn't need any abstract algebra knowledge to be read (I have almost zero knowledge of abstract algebra) and if possible, a book that offers hard problems (like those encountered in olympiads).
Also, I would like to add that, at least right now, I'd like to learn number theory to participate in an olympiad.
I'd also like to add that I didn't consider 104 Number Theory Problems: From the Training of the USA IMO Team because I read somewhere (I think it was in the AoPS site) that it is more a "problem book".
Thank you for your help!
To be honest, I am not sure what "olympiad level" is.
For learning at the elementary level, you might start with this: https://www.amazon.com/Three-Pearls-Number-Theory-Mathematics/dp/0486400263
Then try this: https://www.amazon.com/Number-Theory-Pure-Applied-Mathematics/dp/0121178501#reader_0121178501
This book seems geared specifically for olympiads: https://www.amazon.com/104-Number-Theory-Problems-Training/dp/0817645276/ref=sr_1_2?s=books&ie=UTF8&qid=1471395975&sr=1-2&keywords=olympiad+mathematics+number+theory