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Undergraduate/High-School-Olympiad Level Introductory Number Theory Books For Self-Learning

I took number theory this semester and loved it but don't feel like I learned all that much. I am not going any farther in formal education in math so I would like to further investigate number theory on my own. Do you have any suggestions for good books? I need at least one that is pretty basic and preferably one that goes a little bit more advanced. (You can look at some of my other recent questions to see the level that I'm at, but I really don't understand much beyond Diophantine equations- pretty much have to start over).

I also would prefer if you didn't recommend current textbooks- I've got a pretty small budget. I was looking at Ore's Number Theory and its History, this book, and this book.

Thanks for the help and I apologize if this question is too broad/vague/or subjective.

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marked as duplicate by Qiaochu Yuan May 8 '11 at 3:33

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Two suggestions:

  1. Fundamentals of Number Theory by William Leveque. It's a Dover book, so it'll be reasonably priced.

  2. A Classical Introduction to Modern Number Theory by Kenneth Ireland and Michael Rosen. More pricey (it's a Springer GTM), and pitched at a higher level than LeVeque's.

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I would suggest Solved and Unsolved Problems In number theory by D. Shanks too. – tomerg May 8 '11 at 19:44