On sums of squares of digits

Date of Publication

2009

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

Edmundo R. Perez

Defense Panel Chair

Gaudencio C. Petalcorin, Jr.

Defense Panel Member

Kristine Joy E. Carpio
Mark Oyelle L. Moderno

Abstract/Summary

This paper is an exposition of the work by Beardon [1]. It is basically based on the process of finding out whether or not a natural number is a happy number. For a natural number n, let F(n) be the sum of the squares of the digits of n. If applying F sufficiently many times to n ends in 1, then n is called a happy number. Otherwise, it is said to be an unhappy number. The focus of this paper centers on the fixed points and cycles of F, and the behavior of the function itself. It doesn't matter whether a natural number is a happy number or an unhappy number. Throughout the study, it is encouraged to make simple computer programs in order to verify some results. However, the above definition of F is based on the implicit assumption that numbers are written in base 10. What the study aims to do is to consider the same problem relative to any base.

Abstract Format

html

Language

English

Format

Print

Accession Number

TU15117

Shelf Location

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

Physical Description

v, 31, [8] leaves, 28 cm.

Keywords

Sequences (Mathematics); Number theory

Embargo Period

4-4-2021

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