A New Geometric Method for integer Factorization

The factorization of integers is a central problem in number theory. In this work, we introduce an original method called the LACHKAR method, based on a geometric interpretation of integers as areas. An integer ( N ) is expressed as: [ N = X^2 + R ] We then introduce a parameter ( i ) and study: [ N = (X - i)(X + i) + (R + i^2) ] The method consists in finding values of ( i ) such that: [ \frac{R + i^2}{X - i} \in \mathbb{Z} ] This leads directly to a factorization of ( N ). Compared to classical methods such as Fermat’s factorization, the LACHKAR method introduces additional flexibility and can reduce the number of iterations