MAT 448E - Number Theory

Course Objectives

1-To provide an introduction to the study of properties of integers.
2-To prepare students to graduate-level courses in number theory and algebra.
3-To demonstrate applications of number theory (such as public-key cryptography).

Course Description

Divisibility, Euclidean algorithm,prime numbers,congruences,Chinese remainder theorem,Fermat’s little
theorem,Euler’s theorem primitive roots,congruences with prime-power moduli,Binomial theorem,algebraic
integers,quadratic residues,quadratic reciprocity,Jacobi and Legendre symbols,Euler’s function,Möbius inversion
formula,multiplicative functions,continued fractions,rational approximation,Diophantine equations,Pell’s equation.