Brent, Cohen, and te Riele proved in 1991 that an odd perfect number $ N $ is greater than
$10^{300} $. We modify their method to obtain $ N> 10^{1500} $. We also obtain that $ N …

Number theory is one of the few areas of mathematics where problems of substantial interest
can be fully described to someone with minimal mathematical background. Solving such …

ODD PERFECT NUMBERS HAVE AT LEAST NINE DISTINCT PRIME FACTORS 1.
Introduction A perfect number is one where σ(N) = 2N. In other Page 1 MATHEMATICS OF …

Nowhere in mathematics is the progress resulting from the advent of computers as apparent
as in the additive number theory. In this part, we describe the role of computers in the …

ODD PERFECT NUMBERS HAVE A PRIME FACTOR EXCEEDING 108 1. Introduction A
positive integer n is said to be perfect if σ(n)=2n, wh Page 1 MATHEMATICS OF COMPUTATION …

A positive integer $ n $ is called perfect if $\sigma (n)= 2n $, where $\sigma (n) $ denote the
sum of divisors of $ n $. In this paper we study the ratio $\frac {\sigma (n)}{n} $. We define the …

Using a new factor chain argument, we show that $5 $ does not divide an odd perfect
number indivisible by a sixth power. Applying sieve techniques, we also find an upper …

A perfect number is a positive integer $ N $ such that the sum of all the positive divisors of $
N $ equals $2 N $, denoted by $\sigma (N)= 2N $. The question of the existence of odd …

This book presents material suitable for an undergraduate course in elementary number
theory from a computational perspective. It seeks to not only introduce students to the …

arXiv:1008.0155v1 [math.NT] 1 Aug 2010 Page 1 arXiv:1008.0155v1 [math.NT] 1 Aug 2010
Acta Univ. Sapientiae, Mathematica, 1, 1 (2009) 73–82 Generalized perfect numbers Antal …