On sums of squares of digits

• Main Authors: Santos, J. Loret Q., Sy, Allen G.
• Format: text
• Language: English
• Published: Animo Repository 2009
• Subjects: Sequences (Mathematics); Number theory; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/5227
• Institution: De La Salle University

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.