Mathematics Senior Capstone Papers

Document Type

Article

Publication Date

Spring 2024

Abstract

In the field of number theory, square numbers are very significant, and finding the sums of square numbers is a topic of certain interest to mathematicians. The most immediate application for adding together two square numbers is to identify Pythagorean triples. However, apart from seeking sums of two squares that are squares themselves, interesting patterns emerge that have fascinated number theorists for decades. Particularly, the distribution of a number’s divisors can explicitly determine how many ways that number can be written as a sum of two squares. Furthermore, pentagonal numbers, similar to square numbers, can be visualized by drawing a pentagon with the same number of dots on each side. The purpose of this research is to explore how a theorem concerning the sums of two squares leads to a potential set of characteristics describing the pentagonal numbers.

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