FACTORING POLYNOMIALS IN THE RING OF FORMAL POWER SERIES OVER ℤ
DANIEL BIRMAJER, JUAN B. GIL, MICHAEL WEINER · International Journal of Number Theory · 2012
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.