On the problem σod(n) = σod(n+1)-Reference-Cited by-同舟云学术

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On the problem σod(n) = σod(n+1)

Published:2019 Issue:2 Volume:33 Page:543-559
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Kim Daeyeoul¹,Ikikardes Nazli²,Li Yan³,Ma Lianrong⁴

Affiliation:

1. Department of Mathematics and Institute of Pure and Applied Mathematics, Chon-buk National University, Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do , Republic of Korea

2. Department of Mathematics Education, Necatibey Faculty of Education, Balikesir University, Balikesir, Turkey

3. Department of Applied Mathematics, China Agricultural University, Beijing, China

4. Department of Mathematical Sciences, Tsinghua University, Beijing, China

Abstract

Let ?od(n) = ? d|n,2|?dd. In this paper, we study the solutions of ?od(n) = ?od(n+1), their relations to Pell numbers, and some interesting conjectures. Finally, we obtain that the equation ?od(n) = ?od(n + 1) = ?od(n + 2)?1 (mod 2) has no solution.

Publisher

National Library of Serbia

Subject

General Mathematics

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