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
Accession Number
TU16010
Shelf Location
Archives, The Learning Commons, 12F, Henry Sy Sr. Hall
Physical Description
vi, 96 leaves, 28 cm.
Keywords
Perfect numbers
Recommended Citation
Quintana, N., & Sancho, M. (2010). On some variations of perfect and multiperfect numbers. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/5334
Embargo Period
4-15-2021