A Novel Factorization Method Using Continued Fractions

Abstract

The study of continued fractions is a significant area of mathematics with diverse applications, particularly in the field of factorization. Continued fractions can be used to approximate irrational numbers and are integral to algorithms for factoring integers. In this study, we present a novel method for factoring large integers that utilize generalized continued fractions to improve efficient factorization. Additionally, we introduce several theoretical statements about generalized continued fractions and demonstrate their application within the proposed factorization algorithm. Using this algorithm, we successfully factor a large integer into two prime numbers, whose product constitutes the original large number. Our findings suggest that this method is a highly effective tool in number theory, cryptography, and computational mathematics.