Inequalities about factors of integer polynomials

This resu l t i s t xter than (1) when M ( F ) is not toobig (e.g. for M ( F ) g e t'/d ). It can be very useful in algorithms of factorization of integer polynomials, where inequality (1) is used systematicaly, see Lenstra Lenstra LovAez [ 4 ] for example. Moreover, the case of irreducible factors is the only one used in this paper and our result decreases the cost of this algorithm in an obvious way.