Consider the Mersenne number; $M_p=2^p−1$. Let $M_p=a_pb^2_p$ where $a_p$ is positive, squarefree, and $p$ is prime.

A chinese paper written by Le Maohua "“On Mersenne Numbers”" states that the squarefree part of $M_p$ is greater than $(πp/\log p)^2$.

As the paper is in chinese I could not figure out how the result is obtained. Can someone help me out?

Thank you...

  • 1
    $\begingroup$ Can you give a link to the paper and identify which (of possibly several results in the paper) you are interested in? At the moment it seems that you are asking someone to find and translate or summarize the article for you, which is a lot to ask. $\endgroup$ Apr 21, 2015 at 14:04
  • $\begingroup$ The discussion on mathoverflow.net/questions/149511/… gives some hints for the lower bound of the squarefree part of $a_p$. I am looking for ways to improve the bound. $\endgroup$
    – Kurtul
    Apr 21, 2015 at 14:18
  • $\begingroup$ Could you show the name of the author in Chinese? (the map from characters to pinyin is not injective) $\endgroup$
    – Fan Zheng
    Apr 21, 2015 at 15:24
  • 2
    $\begingroup$ I think the OP talks about MathSciNet entry MR1719617: Le Mao Hua, On Mersenne numbers (Chinese; English, Chinese summary), J. Jishou Univ. Nat. Sci. Ed. 20 (1999), no. 1, 17-19. $\endgroup$
    – GH from MO
    Apr 21, 2015 at 19:53
  • $\begingroup$ @FanZheng It appears to be 乐茂华 (Lè Màohuá). $\endgroup$ Apr 21, 2015 at 23:21


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