What books introduce Number Theory to a Grade 11 student?

I'm in Grade 11. I'm interested in elementary number theory and would like to study it. I'm not intending to enter any competitions.

Solution 1:

Underwood Dudley, Elementary Number Theory, is an excellent introductory text and exceptionally inexpensive. I have heard good things about Joseph H. Silverman, A Friendly Introduction to Number Theory from people whose opinions I respect, but I’ve not seen it myself.

Solution 2:

If you want to study number theory from a solid foundation, I would recommend:

Elementary Number Theory, by David Burton.

It has been used at undergraduate level by universities successfully, and at least the earlier chapters should be well within the ability of a bright school student.

Solution 3:

As a high school kid I got my hands on a copy of Elementary Number Theory: A Problem Oriented Approach by Joe Roberts. I very much enjoyed it then, and really recommend it for self-learning. The book mostly consists of definitions and exercises. Yes, you have to prove the theorems yourself! You can take a peek at the second half for (hints to) solutions though. Another striking feature is that the book is typeset in calligraphy.

Solution 4:

Try "Fermat's Last Theorem," by Simon Singh.

Solution 5:

Ore's Invitation to Number Theory

Art of Problem Solving Introduction to Number Theory.

LeVeque's Fundamentals of Number Theory

Niven and Zuckerman's Introduction to the Theory of Numbers