{"paper":{"title":"On linear combinations of units with bounded coefficients and double-base digit expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel Krenn, J\\\"org Thuswaldner, Volker Ziegler","submitted_at":"2012-05-22T08:05:43Z","abstract_excerpt":"Let $\\ord$ be the maximal order of a number field. Belcher showed in the 1970s that every algebraic integer in $\\ord$ is the sum of pairwise distinct units, if the unit equation $u+v=2$ has a non-trivial solution $u,v\\in\\ord^*$. We generalize this result and give applications to signed double-base digit expansions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4833","kind":"arxiv","version":2},"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"}