Every integer can be written as a square plus a squarefree

Jiménez Urroz, Jorge

doi:10.1016/j.exmath.2021.12.002

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Jiménez Urroz, Jorge

Document typeArticle

Defense date2021-12-30

Rights accessRestricted access - publisher's policy (embargoed until 2023-12-30)

Attribution-NonCommercial-NoDerivs 4.0 International

Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 4.0 International

Abstract

In the paper we can prove that every integer can be written as the sum of two integers, one perfect square and one squarefree. We also establish the asymptotic formula for the number of representations of an integer in this form. The result is deeply related with the divisor function. In the course of our study we get an independent result about it. Concretely we are able to deduce a new upper bound for the divisor function fully explicit.

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CitationJimenez, J. Every integer can be written as a square plus a squarefree. "Expositiones mathematicae", 30 Desembre 2021,

URIhttp://hdl.handle.net/2117/365735

DOI10.1016/j.exmath.2021.12.002

ISSN0723-0869

Publisher versionhttps://www.sciencedirect.com/science/article/abs/pii/S0723086921000748

Other identifiershttps://arxiv.org/abs/2010.15580

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