THE FUNDAMENTAL THEOREM OF ARITHMETIC

The goal here is to formulate the very important Fundamental Theorem of Arithmetic (FTA) and describe some of its history.

1. What is a prime number and what does unique factorization mean? What is the FTA?

2. Explain two examples of 'number systems' in which unique factorization fails.

3. Describe what is meant by a field and then a 'quadratic number field'.

4. Give some of the history of FTA in 1) and 3).

The basic reference is 'An Introduction to the Theory of Numbers' by Niven and Zuckerman. See also 'An Introduction to Number Theory' by H. M. Stark.

Developed by Graham Norton.

http://www.maths.uq.edu.au