• Corpus ID: 116974690

# Solving the Odd Perfect Number Problem: Some Old and New Approaches

@article{Dris2012SolvingTO,
title={Solving the Odd Perfect Number Problem: Some Old and New Approaches},
author={Jose Arnaldo B. Dris},
journal={arXiv: Number Theory},
year={2012}
}

### More on the total number of prime factors of an odd perfect number

• K. Hare
• Mathematics
Math. Comput.
• 2005
This paper extends results to show that n is perfect if a(n) = 2n and defines the total number of prime factors of N as Ω(N):= a + 2Σ k j=1 β j .

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### On the total number of prime factors of an odd perfect number

• Mathematics
Math. Comput.
• 2003
It is proved that if βj ≡ 1 (mod 3) orβj ≡ 2 (mod 5) for all j, 1 ≤ j ≤ k, then 3|n is perfect, where σ(n) denotes the sum of the positive divisors of n.

### On the Largest Prime Divisor of an Odd Perfect Number

• Mathematics
• 1973
It is shown here that if n is odd and perfect, then n has a prime divisor which exceeds 11200. 0. In 1944 Kanold (2) showed that at least one of the /?, is greater than or equal to 61. Our purpose

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This serves as an elementary introduction to the history and theory surrounding even perfect numbers. One would be hard put to find a set of whole numbers with a more fascinating history and more

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### Improved techniques for lower bounds for odd perfect numbers

• Computer Science
• 1989
It is proved here that, subject to certain conditions verifiable in polynomial time, in fact N > q5k/2, and the computations in an earlier paper are extended to show that N > 10300.