{"title":"关于五未知数非齐次五次方程","authors":"Gopalan, G. Sumathi, S. Vidhyalakshmi","doi":"10.22457/jmi.v10a4","DOIUrl":null,"url":null,"abstract":"The non-homogeneous quintic equation with five unknowns represented by x3 + y3 = z3 + w3 +6T5 is considered. Three different patterns of infinitely many non-zero integral solutions of the above the quintic equation are presented. Various interesting realations between the solutions and special number patterns,namely, Polygonal numbers, Star numbers, Centered Polygonal, Jacobsthal lucas numbers and Jacobsthal numbers are exhibited.","PeriodicalId":227898,"journal":{"name":"International Journal of Managment, IT and Engineering","volume":"36 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On the non-homogeneous quintic equation with five unknowns\",\"authors\":\"Gopalan, G. Sumathi, S. Vidhyalakshmi\",\"doi\":\"10.22457/jmi.v10a4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The non-homogeneous quintic equation with five unknowns represented by x3 + y3 = z3 + w3 +6T5 is considered. Three different patterns of infinitely many non-zero integral solutions of the above the quintic equation are presented. Various interesting realations between the solutions and special number patterns,namely, Polygonal numbers, Star numbers, Centered Polygonal, Jacobsthal lucas numbers and Jacobsthal numbers are exhibited.\",\"PeriodicalId\":227898,\"journal\":{\"name\":\"International Journal of Managment, IT and Engineering\",\"volume\":\"36 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-12-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Managment, IT and Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22457/jmi.v10a4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Managment, IT and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22457/jmi.v10a4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the non-homogeneous quintic equation with five unknowns
The non-homogeneous quintic equation with five unknowns represented by x3 + y3 = z3 + w3 +6T5 is considered. Three different patterns of infinitely many non-zero integral solutions of the above the quintic equation are presented. Various interesting realations between the solutions and special number patterns,namely, Polygonal numbers, Star numbers, Centered Polygonal, Jacobsthal lucas numbers and Jacobsthal numbers are exhibited.
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