Consecutive square-free values for some polynomials

Published 6 May 2023 in math.NT | (2305.04020v1)

Abstract: In this paper we study the distribution of consecutive square-free numbers of the forms $x^{2+y^2+z+1$,} $x^{2+y^2+z+2$} and $x^{2+y^{2+z^2+z+1$,}} $x^{2+y^{2+z^2+z+2$,}} respectively. We establish asymptotic formulas for each of these two cases.

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Authors (1)

S. I. Dimitrov

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