Autors: Dimitrov, S. I.
Title: Square-free numbers of the form x^2+y^2+z^2+z+1 and x^2+y^2+z+1
Keywords: square-free number, asymptotic formula, Gauss sum, Salie sum

Abstract: In this paper we study the distribution of square-free positive integers of the form x^2+y^2+z^2+z+1 and x^2+y^2+z+1. We establish asymptotic formulas for the number of triples of positive integers x, y, z ≤ H such that x^2+y^2+z^2+z+1 is square-free and such that x^2+y^2+z+1 is square-free.

References

    Issue

    Math. Notes, vol. 114, issue 6, pp. 1169–1183, 2023, Russia, https://doi.org/10.1134/S0001434623110494

    Вид: статия в списание, публикация в издание с импакт фактор, публикация в реферирано издание, индексирана в Web of Science