# MTH 230, Theory of Numbers

**Note**: If this course is being taught this semester, more
information can be found at the course home page.

## Cross Listed

(none)

## Prerequisites

MTH 172 or MTH 200W or MTH 235

## This course is a prerequisite or co-requisite for

(none)

## Description

The theory of numbers is a broad subject with many connections to other
parts of mathematics as well as to computer science, physics, and
cryptography. It is the study of the properties of the natural numbers.
For example, why does the decimal expansion of 1/7 have period 6 while
that of 1/11 has period 2? Why does x^{2} + y^{2} =
z^{2} have infinitely many solutions in positive integers while
x^{3} + y^{3} = z^{3} has none? Can every
even number greater than 4 be expressed as a sum of two odd primes?
A partial list of the topics we will cover are:

- divisibility theory and Euclidâ€™s algorithm
- the theory of congruences
- the distribution of prime numbers
- primitive roots
- the law of quadratic reciprocity
- sums of squares
- factoring and primality testing
- public key cryptosystems

## Topics covered

Divisibility, primes, congruences, quadratic residues and quadratic reciprocity, primitive roots, elementary prime number theory.