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Paper 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 $O((\alpha-1/4)^{-3/2})$.
Metadata
- Available format(s)
- -- Metadata only -- PS
- Category
- Foundations
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- lattice divisors LLL
- Contact author(s)
- nhowgravegraham @ ntru com
- History
- 2004-12-07: received
- Short URL
- https://ia.cr/2004/339
- License
-
CC BY