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On the largest prime factors of consecutive integers
作者:    时间:2018-06-08 浏览次数:

  

报告人:王志伟博士

报告时间:2018. 6. 9 下午5:00-6:00

报告地点:数学院一楼报告厅


报告摘要:  

Let $P^+(n)$ denote the largest prime factor of the integer $n$. One might guess that the density of integers $n$ with $P^+(n)<P^+(n+1)$ is $1/2$. In fact, this conjecture was formulated in the correspondence of Erd\H{o}s and Tur\'{a}n in the 1930s. More generally, we may consider this type of problem for $k-$consecutive integers with $k\geq 3$, or impose some conditions on the integer $n$. In this talk, we present the progress towards these questions.