Emerging Researchers National (ERN) Conference

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My Journey with Perfect Numbers

Undergraduate #89
Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics

Ayana Tiller - Savannah State University

Mathematicians have been fascinated for centuries by the properties and patterns of numbers. They have noticed that some numbers are equal to the sum of all of their factors (not including the number itself). Such numbers are called perfect numbers. Thus a positive integer is called a perfect number if it is equal to the sum of its proper positive divisors. The search for perfect numbers began in ancient times. The four perfect numbers 6, 28, 496, and 8128 seem to have been known from ancient times. In this paper, we will investigate some important properties of perfect numbers. We give easy and simple proofs of theorems using finite series. We give our own alternative proof of the well-known Euclid’s Theorem (Theorem I). We will also prove some important theorems which play key roles in the mathematical theory of perfect numbers.

Funder Acknowledgement(s): Peach State Louis Stokes Alliance for Minority Participation

Faculty Advisor: Mulatu Lemma,

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This material is based upon work supported by the National Science Foundation (NSF) under Grant No. DUE-1930047. Any opinions, findings, interpretations, conclusions or recommendations expressed in this material are those of its authors and do not represent the views of the AAAS Board of Directors, the Council of AAAS, AAAS’ membership or the National Science Foundation.