On the problem σod(N) = σod(n + 1)

Daeyeoul Kim; Nazli Yildiz Ikikardes; Yan Li; Lianrong Ma

doi:10.2298/FIL1902543K

On the problem σ_od(N) = σ_od(n + 1)

Daeyeoul Kim
, Nazli Yildiz Ikikardes
, Yan Li
, Lianrong Ma

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

Abstract

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

Original language	English
Pages (from-to)	543-559
Number of pages	17
Journal	Filomat
Volume	33
Issue number	2
DOIs	https://doi.org/10.2298/FIL1902543K
State	Published - 2019

Keywords

Congruence
Odd divisor functions

Quacquarelli Symonds(QS) Subject Topics

Mathematics

Access to Document

10.2298/FIL1902543K

Cite this

@article{63e9dc386fae49ed856752e53211cded,

title = "On the problem σod(N) = σod(n + 1)",

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

keywords = "Congruence, Odd divisor functions",

author = "Daeyeoul Kim and Ikikardes, \{Nazli Yildiz\} and Yan Li and Lianrong Ma",

year = "2019",

doi = "10.2298/FIL1902543K",

language = "English",

volume = "33",

pages = "543--559",

journal = "Filomat",

issn = "0354-5180",

number = "2",

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T1 - On the problem σod(N) = σod(n + 1)

AU - Kim, Daeyeoul

AU - Ikikardes, Nazli Yildiz

AU - Li, Yan

AU - Ma, Lianrong

PY - 2019

Y1 - 2019

N2 - Let σod(n) = Σd|n,2†d d. In this paper, we study the solutions of σod(n) = σod(n + 1), their relations to Pell numbers, and some interesting conjectures. Finally, we obtain that the equation σod(n) = σod(n + 1) = σod(n + 2) ≡ 1 (mod 2) has no solution.

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

KW - Congruence

KW - Odd divisor functions

UR - https://www.scopus.com/pages/publications/85066956908

U2 - 10.2298/FIL1902543K

DO - 10.2298/FIL1902543K

M3 - Journal article

AN - SCOPUS:85066956908

SN - 0354-5180

VL - 33

SP - 543

EP - 559

JO - Filomat

JF - Filomat

IS - 2

ER -