# The binary method of integer decomposition

## TL;DR

This paper introduces a novel integer decomposition method that transforms the problem into solving systems of quadratic and linear equations, avoiding guesswork and potentially improving efficiency.

## Contribution

It presents a new approach to integer decomposition by converting it into solving multivariate quadratic and linear equations without guesswork.

## Key findings

- Transforms integer decomposition into solving quadratic equations.
- Reduces problem to solving linear equations with variables up to log2 of the number.
- Offers a direct method without traditional guessing techniques.

## Abstract

This paper presents an integer decomposition method. The method first writes an integer as a polynomial with 2 as variable that its coefficients are zero or one. Then, suppose that an integer is decomposed into product of such two polynomials that their orders are greater than one. By comparing the coefficients of two side, we obtain a system of the multivariate quadratic equations. Therefore, the integer decomposition problem is transformed into the problem of solving a system of the multivariate quadratic equations. Furthermore, the method transforms integer decomposition problem into solving the system of linear equations which the number of variables will not exceed the logarithm with the base of 2 of the decomposed number. The advantage of this method is direct without any guess which is not available in traditional methods.