{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T11:20:33Z","timestamp":1780399233716,"version":"3.54.1"},"reference-count":13,"publisher":"Elsevier BV","issue":"11","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Discrete Mathematics"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.disc.2026.115243","type":"journal-article","created":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T10:20:36Z","timestamp":1780395636000},"page":"115243","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"title":["Note on unique representation bases"],"prefix":"10.1016","volume":"349","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7016-309X","authenticated-orcid":false,"given":"Yuchen","family":"Ding","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.disc.2026.115243_br0010","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1090\/S0025-5718-05-01777-1","article-title":"An old conjecture of Erd\u0151s-Tur\u00e1n on additive bases","volume":"75","author":"Borwein","year":"2006","journal-title":"Math. Comput."},{"key":"10.1016\/j.disc.2026.115243_br0020","first-page":"1","article-title":"An affine analogue of Singer's theorem","volume":"6","author":"Bose","year":"1942","journal-title":"J. Indian Math. Soc."},{"key":"10.1016\/j.disc.2026.115243_br0030","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.ejc.2005.10.004","article-title":"A problem on unique representation bases","volume":"28","author":"Chen","year":"2007","journal-title":"Eur. J. Comb."},{"key":"10.1016\/j.disc.2026.115243_br0040","first-page":"1","article-title":"Solution of a problem of Erd\u0151s and Tur\u00e1n in additive number theory","volume":"14","author":"Chowla","year":"1944","journal-title":"Proc. Natl. Acad. Sci. India Sect. A"},{"key":"10.1016\/j.disc.2026.115243_br0050","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcta.2026.106166","article-title":"Solutions to some problems on unique representation bases","volume":"221","author":"Ding","year":"2026","journal-title":"J. Comb. Theory, Ser. A"},{"key":"10.1016\/j.disc.2026.115243_br0060","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1112\/jlms\/19.76_Part_4.208","article-title":"On a problem of Sidon in additive number theory and on some related problems. Addendum","volume":"19","author":"Erd\u0151s","year":"1944","journal-title":"J. Lond. Math. Soc."},{"key":"10.1016\/j.disc.2026.115243_br0070","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1112\/jlms\/s1-16.4.212","article-title":"On a problem of Sidon in additive number theory, and on some related problems","volume":"16","author":"Erd\u0151s","year":"1941","journal-title":"J. Lond. Math. Soc. (2)"},{"key":"10.1016\/j.disc.2026.115243_br0080","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/S0022-314X(03)00108-2","article-title":"On the Erd\u0151s-Tur\u00e1n conjecture","volume":"102","author":"Grekos","year":"2003","journal-title":"J. Number Theory"},{"key":"10.1016\/j.disc.2026.115243_br0120","series-title":"Sequences","author":"Halberstam","year":"1982"},{"key":"10.1016\/j.disc.2026.115243_br0090","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4064\/aa108-1-1","article-title":"Unique representation bases for the integers","volume":"108","author":"Nathanson","year":"2003","journal-title":"Acta Arith."},{"key":"10.1016\/j.disc.2026.115243_br0100","article-title":"A complete annotated bibliography of work related to Sidon sequences","volume":"11","author":"O'Bryant","year":"2004","journal-title":"Electron. J. Comb."},{"key":"10.1016\/j.disc.2026.115243_br0110","article-title":"A note on a conjecture of Erd\u0151s\u2013Tur\u00e1n","volume":"8","author":"S\u00e1ndor","year":"2008","journal-title":"Integers"},{"key":"10.1016\/j.disc.2026.115243_br0130","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1090\/S0002-9947-1938-1501951-4","article-title":"A theorem in finite projective geometry and some applications to number theory","volume":"43","author":"Singer","year":"1938","journal-title":"Trans. Am. Math. Soc."}],"container-title":["Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X26002670?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X26002670?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T10:52:45Z","timestamp":1780397565000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0012365X26002670"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":13,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2026,11]]}},"alternative-id":["S0012365X26002670"],"URL":"https:\/\/doi.org\/10.1016\/j.disc.2026.115243","relation":{},"ISSN":["0012-365X"],"issn-type":[{"value":"0012-365X","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Note on unique representation bases","name":"articletitle","label":"Article Title"},{"value":"Discrete Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.disc.2026.115243","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115243"}}