Detecting squarefree numbers

TL;DR

This paper introduces a GRH-based algorithm for verifying if an integer is squarefree without full factorization, demonstrating its effectiveness on RSA challenge numbers.

Contribution

The paper presents a novel algorithm leveraging the explicit formula for $L$-functions to determine squarefreeness under GRH, with practical applications.

Findings

Successfully proved several RSA challenge numbers are not squarefull

Algorithm operates efficiently with minimal factorization knowledge

Theoretically analyzed and practically validated the method

Abstract

We present an algorithm, based on the explicit formula for $L$-functions and conditional on GRH, for proving that a given integer is squarefree with little or no knowledge of its factorization. We analyze the algorithm both theoretically and practically, and use it to prove that several RSA challenge numbers are not squarefull.