{"paper":{"title":"On linear equations arising in Combinatorics (Part III)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Masood Aryapoor","submitted_at":"2016-06-25T07:47:33Z","abstract_excerpt":"In the first two papers, the author embarked on a study of classes of linear equations over integers satisfying a \"Farkas-type\" property. As the third paper in this study, the present paper deals with another class of linear equations over integers that has a similar \"Farkas-type\" property. Furthermore it is shown that if an arbitrary system of equations over integers satisfies the conditions imposed by Farkas' lemma then it has rational solutions of a special type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07878","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"}