Introduction to Number Theory

Timetable

Module aim (aims)

Students will be introduced to some of the basic results in Number Theory and their application to solving selected Diophantine equations and congruences and also to public key cryptography.

Pre-requisites in terms of knowledge, skills and social competences (where relevant)

Knowledge of some basic group theory is welcome, though not required.

Syllabus

Primes, Divisibility, the Fundamental Theorem of Arithmetic;Greatest Common Divisor, the extended Euclidean algorithm, modular multiplicative inverse;Congruences, Chinese Remainder Theorem, Euler's theorem, Wilson's theorem;Quadratic Residues and Reciprocity;Diophantine Equations;Sums of squares; Ring of Arithmetic Functions;Public key cryptography.

Reading list

Richard A. Mollin, "Fundamental Number Theory with Applications" (Second Edition) ;K. Ireland and M. Rosen, "A Classical Introduction to Modern Number Theory";MIT open course: https://ocw.mit.edu/courses/mathematics/18-781-theory-of-numbers-spring-2012/