Odd perfect numbers have a prime factor exceeding $10^8$
نویسندگان
چکیده
منابع مشابه
Odd perfect numbers have a prime factor exceeding 108
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.
متن کاملOdd Perfect Numbers Have a Prime Factor Exceeding
It is proved that every odd perfect number is divisible by a prime greater than 107.
متن کاملPerfect Numbers Have a Prime Factor Exceeding 10 7 Paul
It is proved that every odd perfect number is divisible by a prime greater than 107.
متن کاملOdd Perfect Numbers Have a Prime Factor Exceeding 10 7 Paul
It is proved that every odd perfect number is divisible by a prime greater than 107.
متن کاملOdd perfect numbers have at least nine distinct prime factors
An odd perfect number, N , is shown to have at least nine distinct prime factors. If 3 N then N must have at least twelve distinct prime divisors. The proof ultimately avoids previous computational results for odd perfect numbers.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2008
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-08-02050-4