2019 - 22nd Annual Steven Galovich Memorial Student Symposium

Presentation Title

Generalizing Happy Numbers to Fractional Base Number Systems

Student Presenter(s) and Advisor

Mikita Zhylinski, Lake Forest CollegeFollow

Department or Major

Mathematics

Location

Lillard 132

Abstract

Let n be a positive integer and S2 (n) be the sum of the squares of its digits. It is well known that if you iterate S2 enough times you reach a cycle. If one can reach 1 after multiple iterations of S2, 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

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Apr 9th, 10:30 AM Apr 9th, 11:45 AM

Generalizing Happy Numbers to Fractional Base Number Systems

Lillard 132

Let n be a positive integer and S2 (n) be the sum of the squares of its digits. It is well known that if you iterate S2 enough times you reach a cycle. If one can reach 1 after multiple iterations of S2, 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.