Date of Publication

2006

Document Type

Master's Thesis

Degree Name

Master of Science in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Leonor Aquino Ruivivar

Defense Panel Chair

Severino V. Gervacio

Defense Panel Member

Erminda C. Fortes
Yvette F. Lim

Abstract/Summary

This thesis is an exposition of the paper On Perfect Totient Numbers by Douglas E. Iannuci, Deng Moujie and Graeme L. Cohen which appeared in the Journal of Integer Sequences, Vol. 6 (2003), Article 03.4.5. Let n > 2 be a positive integer and let denote Eulers totient function. Define 1(n) = (n) and k(n) = ( k1(n)) for all integers k 2. Define the arithmetic function S by S(n) = (n) + 2(n) + . . . + c(n) + 1, where c(n) = 2. We say n is a perfect totient number if S(n) = n. We give a list of known perfect totient numbers, and we give sufficient conditions for the existence and non-existence of further perfect totient numbers. An original contribution of this study are additional forms of perfect totient numbers.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTG004177

Shelf Location

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

Physical Description

viii, 71 leaves, 28 cm. ; Typescript

Keywords

Perfect numbers; Number theory; Euler's numbers; Arithmetic functions

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