## 2019 - 22nd Annual Steven Galovich Memorial Student Symposium

#### Presentation Title

Generalizing Happy Numbers to Fractional Base Number Systems

#### Department or Major

Mathematics

#### Location

Lillard 132

#### Abstract

Let n be a positive integer and S_{2} (n) be the sum of the squares of its digits. It is well known that if you iterate S_{2} enough times you reach a cycle. If one can reach 1 after multiple iterations of S_{2}, then n is called "happy." The notion of happy numbers has been generalized to different bases, different powers, and even negative bases. In this talk, we consider generalizations to fractional number bases. We will describe what fractional bases are and we'll prove theorems about happy numbers in this setting.

#### Presentation Type

Individual Presentation

#### Start Date

4-9-2019 10:30 AM

#### End Date

4-9-2019 11:45 AM

#### Panel

Research that Counts: Applied Insights and Theoretical Provocations

#### Panel Moderator

DeJuran Richardson

#### Field of Study for Presentation

Mathematics

Generalizing Happy Numbers to Fractional Base Number Systems

Lillard 132

Let n be a positive integer and S_{2} (n) be the sum of the squares of its digits. It is well known that if you iterate S_{2} enough times you reach a cycle. If one can reach 1 after multiple iterations of S_{2}, then n is called "happy." The notion of happy numbers has been generalized to different bases, different powers, and even negative bases. In this talk, we consider generalizations to fractional number bases. We will describe what fractional bases are and we'll prove theorems about happy numbers in this setting.