学术报告

On Some Exponential Diophantine Equations

报告题目:On Some Exponential Diophantine Equations

报告人:祝辉林 博士(厦门大学数学科学学院 副教授)

时间:2019年12月6日(周五)第6,7,8节课,即14:00-14:45, 14: 55-15:40, 16:00-16:45.

地点:讲堂五

报告人简介:祝辉林,厦门大学数学科学学院副教授、硕士生导师,武汉大学博士,山东大学博士后,加拿大英属哥伦比亚大学访问学者。主要从事数论与密码学的研究,特别是丢番图方程、计算数论和密码学算法分析设计及实现等。最近感兴趣的研究主题包括:纯指数三项丢番图方程、广义Lebesgue-Nagell方程、椭圆曲线及超椭圆曲线上的整点、Ljunggren-Nagell方程、Brocard-Ramanujan问题、费马合数、梅森素数、LLL格基约化算法、公钥密码和格密码等。主持国家自然科学基金、福建省自然科学基金和中央高校基本业务项目等多项,曾访问国内外多所著名大学和研究机构,并开展学术交流、合作研究和人才培养。

摘要:In the first part we give a survey about pure ternary exponential Diophantine equations and some developments in results as well as in tools.These tools include Baker''s method, the Bilu-Hanrot-Voutier Theorem about the existence of primitive divisors of Lucas numbers and Lehmer numbers, algebraic number theory methods, and others. We generalize the conjectures of Jesmanowicz, Terai-Cao-Le and Yuan-Han and also present some results that we proved and plan to further improve in this area. Secondly we give some introduction on Fermat numbers and Mersenne numbers, especially their primality test. We hope to find the mathematical structures about a family of composite Fermat numbers and some Mersenne Primes. We approach some related exponential Diophatine equations and get some partial results. Finally we introduce generalized Lebesgue-Ramanujan-Nagell Equations and we will improve in this area.