Odd perfect numbers have at least nine distinct prime factors
نویسندگان
چکیده
منابع مشابه
Odd 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.
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 کاملOdd 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 10 7 Paul
It is proved that every odd perfect number is divisible by a prime greater than 107.
متن کاملOdd Perfect numbers
It is not known whether or not odd perfect numbers can exist. However it is known that there is no such number below 10, (see Brent [1]). Moreover it has been proved by Hagis [4] and Chein [2] independently that an odd perfect number must have at least 8 prime factors. In fact results of this latter type can in principle be obtained solely by calculation, in view of the result of Pomerance [6] ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2007
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-07-01990-4