Odd perfect numbers have a prime factor exceeding 108
نویسندگان
چکیده
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.
منابع مشابه
Odd Perfect Numbers Have a Prime Factor Exceeding
It is proved that every odd perfect number is divisible by a prime greater than 107.
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It is proved that every odd perfect number is divisible by a prime greater than 107.
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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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عنوان ژورنال:
- Math. Comput.
دوره 77 شماره
صفحات -
تاریخ انتشار 2003