Introduction to Number Theory - Solutions Manual

AoPS Introduction Series

by Mathew Crawford

Learn the fundamentals of number theory from former MATHCOUNTS, AHSME, and AIME perfect scorer Mathew Crawford. Topics covered in the book include primes & composites, multiples & divisors, prime factorization and its uses, simple Diophantine equations, base numbers, modular arithmetic, divisibility rules, linear congruences, how to develop number sense, and much more. The text is structured to inspire the reader to explore and develop new ideas. In addition to the instructional material, the book contains hundreds of problems. The solutions manual contains full solutions to nearly every problem, not just the answers. This book is ideal for students who have mastered basic algebra, such as solving linear equations. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of number theory will find this book an instrumental part of their mathematics libraries. About the Mathew Crawford is the founder and CEO of MIST Academy, a school for gifted students, in Birmingham, Alabama. Crawford was a perfect scorer at the national MATHCOUNTS competition in 1990, and a member of the national championship team (Alabama) in 1991. He was a 3-time invitee to the Math Olympiad Summer Program, a perfect scorer on the AIME, and a 2-time USA Math Olympiad honorable mention. 978-0-9773045-4-7 336 pages. 144 pages. Paperback. 10 7/8 x 8 3/8 x 5/8 inches.

Genres: Mathematics, Nonfiction, Number Theory, Textbooks

Paperback

First published January 1, 2006

Reviews

[Calvin · Rating 4 out of 5]

Just finished the book, this is a good intro to number theory which is one of the fields I’m interested in mathematics.

The content covers integers, greatest common divisors, lowest common multiples, primes, numbers in base n, and more primarily, modular arithmetic which is the first time I officially studied the topic. Following that is also linear congruence as well as general tricks in number theory. Overall, an interesting book with challenging problems which most I could understand and do well.

[Peter]

The Introduction to Number Theory is the weakest book in the Art of Problem Solving series. Unlike others there, the difficulty level plateaus early, peaking around Chapter 4 without a satisfying progression. Most topics are covered more thoroughly and with better practice problems in H.S. Hall's Elementary Algebra for Schools. The hints provided are largely unhelpful, often merely reiterating the chapter title, which is already obvious to the reader; at least one hint is outright incorrect.
And the quotes, as usual in AoPS books (with the exception of Precalculus), are rather depressive, anti-rational, and skeptical, along the lines of wondering if one will ever be able to tell where their back ends and their backside begins. Could as well quote St. Augustine: "The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell".

[Ryan · Rating 5 out of 5]

Best intro to number theory I've found. Gives you a very solid foundation to delve deeper into the field. Think my 3 favourite ideas were the fundamental theorem of arithmetic, modular arithmetic and solving linear congruences. Each one completely changes how you look at numbers. Great book.

[Julia · Rating 5 out of 5]

I used this as a text for math... it's probably one of the best books you'll ever come across on the subject. I got a great understanding out of it...

[Bobby Polepalli]

nice