Factorization of quadratic polynomials in the ring of formal power series over Z

Daniel Birmajer; Juan Gil; Michael Weiner

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arXiv · 0706.0725

Factorization of quadratic polynomials in the ring of formal power series over Z

Daniel Birmajer·Juan Gil·Michael Weiner

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Abstract

We establish necessary and sufficient conditions for a quadratic polynomial to be irreducible in the ring $Z[[x]]$ of formal power series with integer coefficients. For $n,m\ge 1$ and $p$ prime, we show that $p^n+p^m\beta x+\alpha x^2$ is reducible in $Z[[x]]$ if and only if it is reducible in $Z_p[x]$, the ring of polynomials over the $p$-adic integers.

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BibTeX RIS

Daniel Birmajer, Juan Gil, Michael Weiner. 2007-06-05. Factorization of quadratic polynomials in the ring of formal power series over Z. https://arxiv.org/abs/0706.0725

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