2017/10/05 by Bober, Jonathan, Fretwell, Dan, Martin, Greg +1
#11N25 #11N32 #12E05 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1710.01970
Given f∈ ℤ[t] of positive degree, we investigate the existence of auxiliary polynomials g∈ ℤ[t] for which f(g(t)) factors as a product of polynomials of small relative degree. One consequence of this work shows that for any quadratic polynomial f∈ℤ[t] and any ε> 0, there are infinitely many n∈ℕ for which the largest prime factor of f(n) is no larger than nε.