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.
 A: 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.
A: 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.
A: 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.
A: Try "Fermat's Last Theorem," by Simon Singh.
A: 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
A: Since you're learning on your own, I'd recommend Elementary Number Theory by Jones and Jones.
A: "Number Theory In Science And Communication" by Manfred R. Schroeder contains a fascinating look at number theory but it isn't really a textbook, it gets my vote.
A: Frank Zorzitto has written a very accessible book on number theory aimed at high school teachers.  It's pretty self-contained and doesn't require a lot of previous experience with proofs.  It also walks through several computer-aided explorations and repeatedly revists the practical problem of cryptography.
At one time you could download it for free from https://amosunov.files.wordpress.com/2017/04/frank-zorzitto-a-taste-of-number-theory.pdf, and the course description for U Waterloo's Math 640 course refers to this as a "free online textbook".
If you use this textbook for a self-study project, you should definitely work through the exercises.  Dr. Zorzitto buries some key concepts in the exercises and relies on you knowing these later.  For example, 'proof by induction' is introduced in an exercise in chapter 1 and is used as a proof mechanism in chapter 2.
A: I recommend Number Theory: Step by Step published in Dec. 2020 by Kuldeep Singh for two reasons. It provides solutions online to EVERY exercise. It uses color.
As Senior Lecturer at University of Hertfordshire, he's taught number theory and linear algebra since Sep 1992 to first and second year undergraduates. I'm not he, but I know of him.
