## Cryptology ePrint Archive: Report 2004/339

**Divisors in Residue Classes, Constructively**

*Don Coppersmith and Nick Howgrave-Graham and S. V. Nagaraj*

**Abstract: **Let $r,s,n$ be integers satisfying $0 \leq r < s < n$,
$s \geq n^{\alpha}$, $\alpha > 1/4$, and $\gcd(r,s)=1$. Lenstra showed that the number of integer divisors of $n$ equivalent to
$r \pmod s$ is upper bounded by $O((\alpha-1/4)^{-2})$. We re-examine this problem; showing how to explicitly construct all such divisors and incidentally improve this bound to $O((\alpha-1/4)^{-3/2})$.

**Category / Keywords: **foundations / lattice divisors LLL

**Date: **received 3 Dec 2004

**Contact author: **nhowgravegraham at ntru com

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | BibTeX Citation

**Version: **20041207:053235 (All versions of this report)

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