INTEGRATION OF NUMBER THEORY WITH COMPUTER ALGEBRA

Abstract

This article explores the integration of number theory with computer algebra systems, examining how these mathematical disciplines enhance each other in modern computational mathematics. We analyze the historical development of this intersection, current methodologies, and emerging applications. The research demonstrates how computer algebra systems have revolutionized number-theoretic investigations by enabling rapid verification of conjectures, discovery of patterns, and proof assistance. Conversely, number theory provides theoretical foundations for many computer algebra algorithms, particularly in cryptography, factorization, and symbolic computation. Through case studies in prime number generation, factorization algorithms, and elliptic curve applications, we illustrate the synergistic relationship between these fields. The findings highlight the importance of this integration for advancing both theoretical mathematics and practical computational tools.