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.
Recommended Citation
Von Tress, Jacob, "An Exploration of the Sums of Two Squares and Pentagonal Numbers" (2024). Mathematics Senior Capstone Papers. 42.
https://digitalcommons.latech.edu/mathematics-senior-capstone-papers/42