勷勤数学•专家报告

题      目：Egyptian fractions with restrictions

报  告  人：陈永高 教授  (邀请人：袁平之)

                                         南京师范大学

时      间： 9月29日  15:30-16:30

地     点：数科院东楼401

报告人简介:

        陈永高，南京师范大学二级教授，博士生导师。2002年获国务院特殊津贴，2007获全国优秀教师称号。曾获第三届钟家庆数学奖，江苏省科技进步奖二等奖等。 多次主持国家自然科学基金面上项目，在国内外著名刊物Amer. J. Math.， J. London Math. Soc.，Math Comp.，J. Number Theory，Acta Arith.，Science China Math.等上发表200多篇论文。曾担任中国数学奥林匹克委员会副主席，多次担任国际数学奥林匹克中国队的领队。

摘      要：

        Egyptian fractions have been extensively studied. In this talk, we will talk about the related progressions on Egyptian fractions.  For any given positive integer k, let T(k) denote the number of representations of one as the sum of k Egyptian fractions with distinct odd denominators. It is clear that T(k)=0 if k is even. In this talk, we give the lower and upper bounds of T(k) for k being odd. We also talk about representations of one as the sum of Egyptian fractions for which all denominators have the given prime factors only.

        欢迎老师、同学们参加、交流！