Number theory, known to Gauss as “arithmetic,” studies the properties of the integers: ... − 3,−2,−1,0,1,2,3.... Although the integers are familiar, and their properties might therefore seem simple, it is instead a very deep subject. For example, here are some problems in number theory that remain unsolved.

This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.

I have included an introduction to most of the topics of elementary number theory. In Sections 1 through 5 the fundamental properties of the integers and congruences are developed, and in Section 6 proofs of Fermat's and Wilson's theorems are given. The number theoretic functions d, cr, and 1> are introduced in Sections 7 to 9. Sections 10 to

Elementary Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from ...

We then introduce the elementary but fundamental concept of a greatest common divisor (gcd) of two integers, and the Euclidean algorithm for finding the gcd of two integers.

Book Title: Elementary Number Theory. Authors: Gareth A. Jones, J. Mary Jones. Series Title: Springer Undergraduate Mathematics Series. DOI: https://doi.org/10.1007/978-1-4471-0613-5. Publisher: Springer London. eBook Packages: Springer Book Archive. Copyright Information: Springer-Verlag London 1998. Softcover ISBN: 978-3-540-76197-6 Published ...

Since number theory is concerned with properties of the integers, we begin by setting up some notation and reviewing some basic properties of the integers that will be needed later:

The 7th Edition offers a presentation that's easier to learn from, while incorporating advancements and recent discoveries in number theory. Expanded coverage of cryptography includes elliptic curve photography; the important notion of homomorphic encryption is introduced, and coverage of knapsack ciphers has been removed.

What Gauss called arithmetic, we now call number theory. This text is an extensive update of an original manuscript by Professor W. Edwin Clark (now Emeritus) of the University of South Florida, written in 2002 and made freely available on his website.

This is a textbook about classical elementary number theory and elliptic curves. The first part discusses elementary topics such as primes, factorization, continued fractions, and quadratic forms, in the context of cryptography, computation, and deep open research problems.