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In this paper we prove that polynomials F(x1,⋯,xn)∈Zx1,⋯,xn of degree d≥3, satisfying certain hypotheses, take on the expected density of (d−1)-free values. This extends the authors' earlier result in 14 where a different method implied the similar statement for polynomials of degree d≥5.
Lapkova et al. (Wed,) studied this question.