2005 Student Research Conference:

18th Annual Student Research Conference

18th Annual Student Research Conference

**Fermat's Last Theorem and the Development of Algebraic Number Theory**

Melissa J. Allen

Prof. Tony Vazzana, Faculty Mentor

Gabriel Lamé thought he was on the verge of proving Fermat's Last Theorem in 1847, but Ernst Kummer had found a flaw in his method a few years earlier. A new branch of mathematics, algebraic number theory, was developed through Lamé’s faulty proof. A brief overview of early attempts to prove Fermat's Last Theorem and discussion of unique factorization will give the audience some background. We will then outline the strategy proposed by Lamé and explain why unique factorization was a stumbling block. We will also explain Kummer's new ‘numbers’ that he used to prove Fermat's Last Theorem for all regular primes.

**Keywords:** Fermat, Last Theorem, number theory, algebra, unique factorization

**Topic(s):**Mathematics

**Presentation Type:** Oral Paper

**Session:** 8-2

**Location:** VH 1408

**Time:** 8:30