{"paper":{"title":"On the smallest number of terms of vanishing sums of units in number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrzej Schinzel, Csan\\'ad Bert\\'ok, K\\'alm\\'an Gy\\H{o}ry, Lajos Hajdu","submitted_at":"2018-06-01T11:50:28Z","abstract_excerpt":"Let $K$ be a number field. In the terminology of Nagell a unit $\\varepsilon$ of $K$ is called {\\it exceptional} if $1-\\varepsilon$ is also a unit. The existence of such a unit is equivalent to the fact that the unit equation $\\varepsilon_1+\\varepsilon_2+\\varepsilon_3=0$ is solvable in units $\\varepsilon_1,\\varepsilon_2,\\varepsilon_3$ of $K$. Numerous number fields have exceptional units. They have been investigated by many authors, and they have important applications.\n  In this paper we deal with a generalization of exceptional units. We are interested in the smallest integer $k$ with $k\\geq "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00296","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"}