A Graph-Theoretic Proof of the Fundamental Theorem of Arithmetic with Algorithmic Construction

Hitesh Choudhury

Abstract: The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be factored uniquely into prime numbers, up to order. In this paper, we present a graph-theoretic framework to understand and prove this theorem. By modeling factorization as a tree structure, we define factorization trees and establish four supporting lemmas. We then develop a recursive algorithm for constructing these trees. This approach not only yields a constructive proof of the theorem but also offers visual and algorithmic insights into the uniqueness of prime factorizations.

Keywords: Fundamental Theorem of Arithmetic, Graph Theory, Factorization Tree, Prime Factorization, Directed Acyclic Graph, Number Theory Algorithm

How to Cite?: Hitesh Choudhury, "A Graph-Theoretic Proof of the Fundamental Theorem of Arithmetic with Algorithmic Construction", Volume 14 Issue 6, June 2025, International Journal of Science and Research (IJSR), Pages: 602-603, https://www.ijsr.net/getabstract.php?paperid=SR25608225333, DOI: https://dx.doi.org/10.21275/SR25608225333