#### Description

Integers, divisibility, prime numbers, unique factorization, congruences, quadratic reciprocity, Diophantine equations and arithmetic functions.

#### Prerequisites

A C- or better in one of MATH 240, MATH 241, MATH 246, MATH 340, or MATH 341

#### Topics

**The integers**

Divisibility

Prime numbers

Greatest common divisor

Euclidean algorithm

Unique factorization

**Congruences**

Basic properties

Modular arithmetic

Euler's phi function

Fermat's, Euler's and Wilson's theorems

Chinese remainder theorem

**Quadratic Reciprocity**

Quadratic residues

Legendre and Jacobi symbols

Law of quadratic reciprocity (possibility skip proof to allow time for other topics)

**Additional Topics, (as time allows)**

Diophantine equations: Pythagoras, Fermat, Pell

Primitive roots: Lagrange's Theorem

Primality testing

Factoring

RSA Algorithm

Arithmetic functions, Moebius inversion formula, Mersenne primes