I am studying research paper " A note on odd zeta values " by Tanguy Rivoal and Wadim Zudilin . 

>Note-> This question has been closed 2 times on math.stackexchange . Earlier it was posted on MathOverflow but people here said it should be posted on math stackexchange. But  they have closed it 2 times consecutively.

>Please help I am badly struck on it. 

Notations:
[![enter image description here][1]][1]


>I couldn't think about how authors write the equation - we obtain $\phi_{(n) }^{-1} ( F(t) (t+m)^5 )_{ t=-m} $ $ \in \mathbb{Z} $ for m= 0 ,1,...,n by defininig $\phi_{(n)} = \prod_{2√n<p\leq n } p^{\rho_0(n/p) } $ .

Kindly see last 2 lines of image posted below , I have underlined(in black) the part in which i have question .[![enter image description here][2]][2]



[![enter image description here][3]][3]
 



I have understood everything in research paper till this argument but  I don't have a clue on how authors derives the underlined part. 

>I think  they are using [12, lemma1] (Paper-" One of odd zeta values from $\zeta(5)$ to $\zeta(25) $ is irrational by elementary means " By Wadim Zudilin )whose image I am posting below but unfortunately  I am not able to obtain this relation from the lemma. 
Image of lemma ->

[![enter image description here][4]][4]


It would be really helpful for me if anyone can tell me  how to deduce this equation  $\phi_{(n) }^{-1} ( F(t) (t+m)^5 )_{ t=-m} $ $\in \mathbb{Z}$?


 


  [1]: https://i.sstatic.net/UsIUs.png
  [2]: https://i.sstatic.net/9lPrR.png
  [3]: https://i.sstatic.net/5JQJB.png
  [4]: https://i.sstatic.net/20d0h.png