A Generalization of Lehman's Method

TL;DR

This paper introduces a new deterministic algorithm for finding square and r-power divisors based on Lehman's method, which is simple to implement and effective with known bounds, and explores its adaptation to other factorization algorithms.

Contribution

It generalizes Lehman's method for r-power divisors and addresses its adaptation to recent deterministic factorization algorithms.

Findings

Effective when a loose bound on a square divisor is known

Can find r-power divisors efficiently

Addresses adaptation of recent algorithms for r-power divisors

Abstract

A new deterministic algorithm for finding square divisors, and finding $r$-power divisors in general, is presented. This algorithm is based on Lehman's method for integer factorization and is straightforward to implement. While the theoretical complexity of the new algorithm is far from best known, the algorithm becomes especially effective if even a loose bound on a square divisor is known. Additionally, we answer a question by D. Harvey and M. Hittmeir on whether their recent deterministic algorithm for integer factorization can be adapted to finding $r$-power divisors.