{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:11:06Z","timestamp":1760231466520,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,16]],"date-time":"2022-09-16T00:00:00Z","timestamp":1663286400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Foundation of Liaoning Educational Committee","award":["2019LNJC08"],"award-info":[{"award-number":["2019LNJC08"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we show that 66666 is the largest repdigit expressible as the sum of four tribonacci numbers. We used Binet\u2019s formula, Baker\u2019s theory, and a reduction method during the proving procedure. We also used the periodic properties of tribonacci number modulo 9 to deal with three individual cases.<\/jats:p>","DOI":"10.3390\/sym14091931","type":"journal-article","created":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T04:28:55Z","timestamp":1663648135000},"page":"1931","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Repdigits as Sums of Four Tribonacci Numbers"],"prefix":"10.3390","volume":"14","author":[{"given":"Yuetong","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Science, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3096-2254","authenticated-orcid":false,"given":"Peng","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Science, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4876-6000","authenticated-orcid":false,"given":"Shaonan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Science, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8810-2041","authenticated-orcid":false,"given":"Kaiqiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Science, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,16]]},"reference":[{"key":"ref_1","first-page":"356","article-title":"Une propr\u00e9t\u00e9 des puissances parfaites","volume":"65","year":"1956","journal-title":"Mathesis"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1112\/S0025579300007865","article-title":"On integers with identical digits","volume":"46","author":"Bugeaud","year":"1999","journal-title":"Mathematika"},{"key":"ref_3","first-page":"242","article-title":"Fibonacci and Lucas Numbers with Only One Distinct Digit","volume":"57","author":"Luca","year":"2000","journal-title":"Port. 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Hungar."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1515\/ms-2017-0371","article-title":"Repdigits as sums of three balancing numbers","volume":"70","author":"Ddamulira","year":"2020","journal-title":"Math. Slovaca"},{"key":"ref_9","first-page":"Article 18.7.7","article-title":"Repdigits as Sums of Four Fibonacci or Lucas Numbers","volume":"21","author":"Normenyo","year":"2018","journal-title":"J. Integer Seq."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s40590-018-0202-1","article-title":"Repdigits as sums of four Pell numbers","volume":"25","author":"Luca","year":"2019","journal-title":"Bol. Soc. Mat. Mex."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"55","DOI":"10.21136\/MB.2020.0077-19","article-title":"Repdigits in the base b as sums of four balancing numbers","volume":"146","author":"Keskin","year":"2021","journal-title":"Math. 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