This question is related to Paper of Wadim Zudilin and Tanguy Rivoal "A note on odd zeta values".

Some users are saying that I should not post question related to papers in MO but site mentions questions from graduate text books and papers could be asked. Please give some hint and a question easy to you might not necessarily be easy to me .

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I am unable to prove in last line of 4 th image how $(\phi_{n})^{-3} {d_n}^{A+2} q_{j,n}$ is an integer for odd j $\geq$ 5 but first part for $j=0$ I could prove.

I tried 2nd part 3 times but could not prove it. Can someone please help.