GCD, prime and composite numbers, factorisation of numbers, fundamental theorem of arithmetic 3 lectures Residues, Euler's quotient function, Euler-Fermat theorems, Chinese Remainder theorem.

Method of Fermat descent. Fermat and Lagrange theorems. Prerequisites For details of prerequisites, corequisites, excluded combinations, teaching methods, and assessment details, please see the Faculty Handbook.

## Elementary Number Theory with Applications - 2nd Edition

Examination Information For information about use of calculators and dictionaries in exams please see the Examination Information page in the Degree Programme Handbook. Applications of number theory are well integrated into the text, illustrating the usefulness of the theory. Computer exercises and projects in each section of the text cover specific concepts or algorithms from that section, guiding students on combining the mathematics with their computing skills. Cryptography and cryptographic protocols are covered in depth.

This is the first number theory text to cover cryptography, and results important for cryptography are developed with the theory in the early chapters.

### Submission history

The flexible organization allows instructors to choose from a wealth of topics when designing a course. Historical content and biographies illustrate the human side of number theory, both ancient and modern. Careful proofs explain and support a number of the key results of number theory, helping students develop their understanding.

The Companion Website www. The Instructor's Solution Manual available for download from the Pearson Instructor Resource Center provides complete solutions to all exercises, material on programming projects, and an extensive test bank. Applets on the Companion Website involve some common computations in number theory and help students understand concepts and explore conjectures.

Additionally, a collection of cryptographic applets is also provided. New to This Edition. Many new discoveries, both theoretical and numerical, are introduced.

## MATH2617 Elementary Number Theory II

Coverage includes four Mersenne primes, numerous new world records, and the latest evidence supporting open conjectures. Recent theoretical discoveries are described, including the Tao-Green theorem about arbitrarily long arithmetic progressions of primes. This edition also includes historical information about secret British cryptographic discoveries that predate the work of Rivest, Shamir, and Adelman.

Expanded treatment of both resolved and open conjectures about prime numbers is provided.

## Category:Elementary number theory

Combinatorial number theory —partitions are covered in a new section of the book. This provides an introduction to combinatorial number theory, which was not covered in previous editions.

This new section covers many aspects of this topics including Ferrers diagrams, restricted partition identities, generating functions, and the famous Ramanujan congruences. Partition identities are proved using both generating functions and bijections. Congruent numbers and elliptic curves —a new section is devoted to the famous congruent number problem, which asks which positive integers are the area of a right triangle with rational side lengths.

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This section shows that the congruent number problem is equivalent to finding rational points on certain elliptic curves and introduces some basic properties of elliptic curves. The use of geometric reasoning in the solution of diophantine problems has been added to the new edition. In particular, finding rational points on the unit circle is shown to be equivalent to finding Pythgaorean triples.

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Evaluation Copy Request an Evaluation Copy. This is a dummy description. A highly successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming.