On some variations of perfect and multiperfect numbers

Date of Publication

2010

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with specialization in Business Applications

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Leonor A. Ruivivar

Defense Panel Chair

Anita C. Ong

Defense Panel Member

Sonia Y. Tan
Christopher Thomas R. Cruz

Abstract/Summary

A positive integer is said to be perfect if the sum of its divisors is twice the number. This paper is a partial exposition of the articles On Multiply Perfect Numbers with a Special Property by Carl Pomerance (1975), Variations on Euclid's Formula for Perfect Numbers by Farideh Firoozbakt (2010), and Iterating the Sum-of-Divisors Function by Graeme Cohen and Herman te Riele. The paper deals with different variations of perfect numbers. The first major result determined solutions to a problem involving the sum-of-divisors function satisfying certain conditions. The results showed that all solutions are multiperfect numbers, a generalization of perfect numbers in which the sum of the divisors is a positive integral multiple of the number. The second article dealt with generalizing the concept of multiperfect numbers by iterating the sum-of-divisors function σ, giving rise to what we call (m,k)-perfect numbers. One of the questions that was attempted to e answered was Are all numbers (m,k)-perfect? It was shown that numbers up to 1000 are (m,k)-perfect. The third article gave solutions to various variations of Euclid's equation of the form σ(x), = kx + f(x), where k is an integer larger than 1 and f is an arithmetic function of x.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU16010

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

vi, 96 leaves, 28 cm.

Keywords

Perfect numbers

Embargo Period

4-15-2021

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