Consecutive square-free values for some polynomials

2023/05/06 by Dimitrov, S. I.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2305.04020

Abstract

In this paper we study the distribution of consecutive square-free numbers of the forms x²+y²+z+1, x²+y²+z+2 and x²+y²+z²+z+1, x²+y²+z²+z+2, respectively. We establish asymptotic formulas for each of these two cases.

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