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Implications of representative of $p$-adic factor $g$ of $f$ dividing $f$ in $\mathbb{Z}[X]$

The problem is from this paper (click for pdf) by Mark van Hoeij. Let $f \in \mathbb{Z}[X]$ be monic and squarefree. Let $B$ be a Landau-Mignotte bound for $f$, i.e. for any rational factor $\phi$ ...
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