{"paper":{"title":"Worst-Case Analysis of Weber's Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Christian Lavault (LIPN), Sidi Mohamed Sedjelmaci (LIPN)","submitted_at":"2013-11-28T16:52:43Z","abstract_excerpt":"Recently, Ken Weber introduced an algorithm for finding the $(a,b)$-pairs satisfying $au+bv\\equiv 0\\pmod{k}$, with $0<|a|,|b|<\\sqrt{k}$, where $(u,k)$ and $(v,k)$ are coprime. It is based on Sorenson's and Jebelean's \"$k$-ary reduction\" algorithms. We provide a formula for $N(k)$, the maximal number of iterations in the loop of Weber's GCD algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7369","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}