On the Applications of Cyclotomic Fields in Introductory Number Theory

Berkeley Scientific: the journal of young scientists

article

Kabalan Gaspard¹ 

[1] Mathematical Institute, Oxford University

关键词: Number Theory;    Cyclotomic Fields;    Pell's Equation;    Dirichlet;    Kummer;    Fermat's Last Theorem;    Primary Units;    Real Units;   

DOI  :  10.5070/BS3171016284

学科分类：社会科学、人文和艺术（综合）

来源: University of California, Berkeley

【 摘 要 】

In this essay, we study and comment on two number theoretical applications on prime cyclotomic fields (cyclotomic fields obtained by adjoining a primitive p-th root of unity to Q, where p is an odd prime). We begin by giving a simplified proof of Kummer's case of Fermat's Last Theorem obtained by linking different versions of the proof in different textbooks. We finally modernize Dirichlet's solution to Pell's Equation.

【 授权许可】

Unknown