# Polynomial factorization over ℤ[X]

• Guy Viry
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 229)

## Abstract

This paper gives a new method of factorization of a polynomial P over ℤ. The method is grounded on the fact, that any squarefree polynomial has a simple p-adic root. The algorithm starts from a simple root of P over ℤ/pℤ and from this root the algorithm computes the corresponding root of P over ℤ/pk ℤ, using Newton's method. So we obtain a linear factor of P.

Afterwards, as Lenstra in [3], we search for a polynomial Q which is a multiple of this linear factor and which has sufficiently small coefficients. If k is sufficiently large, then Q is a divisor of P over ℤ.

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