{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:35:36Z","timestamp":1746804936597,"version":"3.40.5"},"reference-count":6,"publisher":"Wiley","license":[{"start":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T00:00:00Z","timestamp":1562630400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Summer Undergraduate Research Program","award":["SURE PLUS 2017","31S267 (G00002400)"],"award-info":[{"award-number":["SURE PLUS 2017","31S267 (G00002400)"]}]},{"DOI":"10.13039\/501100006013","name":"United Arab Emirates University","doi-asserted-by":"publisher","award":["SURE PLUS 2017","31S267 (G00002400)"],"award-info":[{"award-number":["SURE PLUS 2017","31S267 (G00002400)"]}],"id":[{"id":"10.13039\/501100006013","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2019,7,9]]},"abstract":"<jats:p>We prove the polynomial analogues of some Liouville identities from elementary number theory. Consequently several sums defined over the finite fields <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">F<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">[<\/mml:mo><mml:mi>t<\/mml:mi><mml:mo stretchy=\"false\">]<\/mml:mo><\/mml:math> are evaluated by combining the results obtained and some of the results from sums of reciprocals of polynomials over <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">F<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">[<\/mml:mo><mml:mi>t<\/mml:mi><mml:mo stretchy=\"false\">]<\/mml:mo><\/mml:math>.<\/jats:p>","DOI":"10.1155\/2019\/2896847","type":"journal-article","created":{"date-parts":[[2019,7,9]],"date-time":"2019-07-09T19:30:37Z","timestamp":1562700637000},"page":"1-7","source":"Crossref","is-referenced-by-count":0,"title":["Evaluation of Some Sums of Polynomials in <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:msub><mml:mrow><mml:mi mathvariant=\"double-struck\">F<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">[<\/mml:mo><mml:mi>t<\/mml:mi><mml:mo stretchy=\"false\">]<\/mml:mo><\/mml:math>"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6164-7308","authenticated-orcid":true,"given":"Adama","family":"Diene","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, United Arab Emirates University, PO Box 17551, Al-Ain, UAE"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-6046-0"},{"year":"2011","series-title":"Cambridge University Press","key":"2"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-35-00114-4"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2014.08.004"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.4169\/amer.math.monthly.119.04.313"},{"issue":"2, article no. 2","key":"6","volume":"17","year":"2016","journal-title":"Rose-Hulman Undergraduate Mathematics Journal"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2019\/2896847.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2019\/2896847.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2019\/2896847.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,21]],"date-time":"2019-09-21T14:41:15Z","timestamp":1569076875000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/jam\/2019\/2896847\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,9]]},"references-count":6,"alternative-id":["2896847","2896847"],"URL":"https:\/\/doi.org\/10.1155\/2019\/2896847","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2019,7,9]]}}}