Factoring polynomials in the ring of formal power series over Z

We consider polynomials with integer coefficients and discuss their factorization properties in [[x]], the ring of formal power series over . We treat polynomials of arbitrary degree and give sufficient conditions for their reducibility as power series. Moreover, if a polynomial is reducible over [[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.