# Detecting squarefree numbers

arXiv: https://arxiv.org/abs/1304.6937 · HTML: https://mlsanity.com/paper/1304.6937/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2013.

## Built on by (most cited first, 2 of 2)

- [Studying number theory with deep learning: a case study with the M"obius and squarefree indicator functions](https://mlsanity.com/paper/2502.10335/) (2025)
- [Reconstructing Test Labels from Noisy Loss Functions](https://mlsanity.com/paper/2107.03022/) (2021)

## Abstract (arXiv)

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.