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arXiv · 1308.2987

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

Daniel Birmajer·Juan B. Gil·Michael D. Weiner
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Abstract

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

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Daniel Birmajer, Juan B. Gil, Michael D. Weiner. 2013-08-13. On Hensel's roots and a factorization formula in Z[[x]]. https://arxiv.org/abs/1308.2987

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