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Divisors in Residue Classes, Constructively
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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 $O((\alpha-1/4)^{-3/2})$. |
BibTeX
@misc{eprint-2004-12303, title={Divisors in Residue Classes, Constructively}, booktitle={IACR Eprint archive}, keywords={foundations / lattice divisors LLL}, url={http://eprint.iacr.org/2004/339}, note={ nhowgravegraham@ntru.com 12755 received 3 Dec 2004}, author={Don Coppersmith and Nick Howgrave-Graham and S. V. Nagaraj}, year=2004 }