20190806, 01:32  #1 
Aug 2019
11 Posts 
Help : Deriving an inequality
Hi, I am studying a paper by Yann Bugeaud (click here), on page 13 there is an inequality (16) as given below image
https://www.mersenneforum.org/attach...1&d=1565055006 which is obtained from the below image file  https://www.mersenneforum.org/attach...1&d=1565055006 , on page 12. How the inequality (16) is derived? I couldn't figure it out. However one of my forum member tried but it has two problems (problems are marked as "how?"), it is given in below image https://www.mersenneforum.org/attach...1&d=1565055006 It is not clear how those two questions would be resolved. Can any one show the derivation of inequality (16)? Thanks in Advance. 
20190806, 03:07  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
5×7×263 Posts 
So, you didn't find help over here:
https://www.freemathhelp.com/forum/t...quence.117311/ Since the post is identical except the image attachments it looks like you copied and pasted. Can you give us some more background? 
20190806, 04:51  #3 
Aug 2019
B_{16} Posts 
No I did not get any help from there, you can find all detail in page 12 an 13 of the paper, not much detail is given.

20190806, 22:51  #4 
Feb 2017
Nowhere
2^{4}×3^{2}×29 Posts 
The symbol isn't just an inequality symbol. In analytic number theory, if f and g are functions of one variable (in particular, a positive integer variable)
indicates that there is a (positive) constant k such that for sufficiently large n. The notation is due to Vinogradov. 
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