{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T17:41:54Z","timestamp":1757612514509,"version":"3.44.0"},"reference-count":19,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,9,11]],"date-time":"2021-09-11T00:00:00Z","timestamp":1631318400000},"content-version":"vor","delay-in-days":253,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>This paper presents a new approach to determine the number of solutions of three\u2010variable Frobenius\u2010related problems and to find their solutions by using order reducing methods. Here, the order of a Frobenius\u2010related problem means the number of variables appearing in the problem. We present two types of order reduction methods that can be applied to the problem of finding all nonnegative solutions of three\u2010variable Frobenius\u2010related problems. The first method is used to reduce the equation of order three from a three\u2010variable Frobenius\u2010related problem to be a system of equations with two fixed variables. The second method reduces the equation of order three into three equations of order two, for which an algorithm is designed with an interesting open problem on solutions left as a conjecture.<\/jats:p>","DOI":"10.1155\/2021\/6396792","type":"journal-article","created":{"date-parts":[[2021,9,11]],"date-time":"2021-09-11T13:35:08Z","timestamp":1631367308000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Solutions of Three\u2010Variable Frobenius\u2010Related Problems Using Order Reduction Approach"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9405-5808","authenticated-orcid":false,"given":"Tian-Xiao","family":"He","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter J.-S.","family":"Shiue","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rama","family":"Venkat","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,9,11]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.2020.1707625"},{"key":"e_1_2_6_2_2","article-title":"Maths quest","volume":"41","author":"Sylvester J. 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