Odd perfect numbers have a prime factor exceeding 10

Takeshi Goto; Yasuo Ohno

doi:10.1090/S0025-5718-08-02050-4

Odd perfect numbers have a prime factor exceeding 10

Takeshi Goto, Yasuo Ohno

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

Jenkins in 2003 showed that every odd perfect number is divisible by a prime exceeding 10⁷. Using the properties of cyclotomic polynomials, we improve this result to show that every perfect number is divisible by a prime exceeding 10⁸.

Original language	English
Pages (from-to)	1859-1868
Number of pages	10
Journal	Mathematics of Computation
Volume	77
Issue number	263
DOIs	https://doi.org/10.1090/S0025-5718-08-02050-4
Publication status	Published - 2008 Jul
Externally published	Yes

Keywords

Cyclotomic numbers
Odd perfect numbers

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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10.1090/S0025-5718-08-02050-4

Cite this

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title = "Odd perfect numbers have a prime factor exceeding 10",

abstract = "Jenkins in 2003 showed that every odd perfect number is divisible by a prime exceeding 107. Using the properties of cyclotomic polynomials, we improve this result to show that every perfect number is divisible by a prime exceeding 108.",

keywords = "Cyclotomic numbers, Odd perfect numbers",

author = "Takeshi Goto and Yasuo Ohno",

year = "2008",

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doi = "10.1090/S0025-5718-08-02050-4",

language = "English",

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pages = "1859--1868",

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AU - Ohno, Yasuo

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KW - Cyclotomic numbers

KW - Odd perfect numbers

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JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 263

ER -

Odd perfect numbers have a prime factor exceeding 10

Abstract

Keywords

ASJC Scopus subject areas

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