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Paper: Divisors in Residue Classes, Constructively

Authors:
Don Coppersmith
Nick Howgrave-Graham
S. V. Nagaraj
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URL: http://eprint.iacr.org/2004/339
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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
}