Odd Perfect Numbers Have At Least Nine Distinct Prime Factors

Details Odd Perfect Numbers Have At Least Nine Distinct Prime Factors Odd Perfect Numbers Have At Least Nine Distinct Prime Factors

2006-02-22

arxiv.org/abs/math/0602485v1

Mathematics

Number Theory

17 pages

Scientific paper

10.1090/S0025-5718-07-01990-4

An odd perfect number, N, is shown to have at least nine distinct prime
factors. If 3 does not divide 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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