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# Number Theory: Course Outline (MAT 464)

The branch of mathematics that deals with the properties and relationships of numbers, especially the positive integers.

## Course Objective

This course will strengthen each student's ability to use theory to solve concrete problems in number theory. Application of abstract algebra interms of number theory will enable student to apply these techniques to solve different problems in number theory.

## Course Contents

Divisibility: Divisors, Bezeout’s identity, LCM, Linear Diophantine equations,

Prime Numbers: Prime numbers and prime-power factorizations, Distribution of primes, Primality-testing and factorization,

Congruences: Modular arithmetic, Linear congruences, An extension of chineses Remainder Theorem, The Arithmetic’s of Zp. Solving conruences mod (pe). Euler’s Function: Units, Euler’s function,

The Group of Units: The group Un, Primitive roots, The group Un, n is power of odd prime and n is power of 2,