4 research outputs found
Factorization of quadratic polynomials in the ring of formal power series over
We establish necessary and sufficient conditions for a quadratic polynomial
to be irreducible in the ring of formal power series with integer
coefficients. For and prime, we show that is reducible in if and only if it is reducible in , the
ring of polynomials over the -adic integers.Comment: 15 page
Factoring polynomials in the ring of formal power series over Z
We consider polynomials with integer coefficients and discuss their
factorization properties in Z[[x]], the ring of formal power series over Z. We
treat polynomials of arbitrary degree and give sufficient conditions for their
reducibility as power series. Moreover, if a polynomial is reducible over
Z[[x]], we provide an explicit factorization algorithm. For polynomials whose
constant term is a prime power, our study leads to the discussion of p-adic
integers.Comment: 10 pages, submitte