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Given an odd prime $p$, we provide formulas for the Hensel lifts ofpolynomial roots modulo $p$, and give an explicit factorization over the ringof formal power series with integer coefficients for certain reduciblepolynomials whose constant term is of the form $p^w$ with $w>1$. All of ourformulas are given in terms of partial Bell polynomials and rely on theinversion formula of Lagrange.

On Hensel's roots and a factorization formula in Z[[x]]