On the Determination of Happy Numbers

Abstract

INTRODUCTION

The primary objective of the paper is to focus on happy numbers. It intends to present the iteration of the set of positive integers, determines the fixed points and cycles of positive integers, and develop a computer program.

METHODS

The researcher consulted peers and experts on happy numbers and read books, journals and electronic referencing in conducting the study. Microsoft Visual Studio was also utilized.

RESULTS

The researcher determined different fixed points and cycles through iteration to the sum of its fourth power. Through a computer program, happy numbers were identified and it was proven that when the interval becomes larger, the density of happy number becomes smaller.

DISCUSSIONS

Through a computer program, happy numbers were identified; and it was proven that when the interval becomes larger, the density of the happy number becomes smaller.