{"title":"关于5未知数齐次双二次方程","authors":"P. Jayakumar, J. Meena","doi":"10.21275/v4i12.nov151842","DOIUrl":null,"url":null,"abstract":"The Homogenous biquadratic equation with five unknowns given by 2 2 2 4 4 ) ( 26 R w z y x is considered and analyzed for finding its non zero distinct integral solutions. Introducing the linear transformations x = u + v, y = u – v, z = 2uv +1, w =2uv-1 and employing the method of factorization different patterns of non zero distinct integer solutions of the equation under the above equation are obtained. A few interesting relations between the integral solutions and the special numbers namely Polygonal numbers, Star number, Pronic number and Gnomonic number are exhibited.","PeriodicalId":13846,"journal":{"name":"International Journal for Scientific Research and Development","volume":"49 1","pages":"204-206"},"PeriodicalIF":0.0000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On The Homogeneous Biquadratic Equation with 5 Unknowns\",\"authors\":\"P. Jayakumar, J. Meena\",\"doi\":\"10.21275/v4i12.nov151842\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Homogenous biquadratic equation with five unknowns given by 2 2 2 4 4 ) ( 26 R w z y x is considered and analyzed for finding its non zero distinct integral solutions. Introducing the linear transformations x = u + v, y = u – v, z = 2uv +1, w =2uv-1 and employing the method of factorization different patterns of non zero distinct integer solutions of the equation under the above equation are obtained. A few interesting relations between the integral solutions and the special numbers namely Polygonal numbers, Star number, Pronic number and Gnomonic number are exhibited.\",\"PeriodicalId\":13846,\"journal\":{\"name\":\"International Journal for Scientific Research and Development\",\"volume\":\"49 1\",\"pages\":\"204-206\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal for Scientific Research and Development\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21275/v4i12.nov151842\",\"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 for Scientific Research and Development","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21275/v4i12.nov151842","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
考虑并分析了由2 2 2 4 4)(26 R w z y x 给出的五未知数齐次双二次方程的非零离散积分解。引入线性变换x = u + v, y = u - v, z =2uv +1, w =2uv-1，采用因式分解的方法，得到了上述方程的非零异整数解的不同形式。给出了积分解与多边形数、星数、质子数、Gnomonic数等特殊数之间的一些有趣的关系。
On The Homogeneous Biquadratic Equation with 5 Unknowns
The Homogenous biquadratic equation with five unknowns given by 2 2 2 4 4 ) ( 26 R w z y x is considered and analyzed for finding its non zero distinct integral solutions. Introducing the linear transformations x = u + v, y = u – v, z = 2uv +1, w =2uv-1 and employing the method of factorization different patterns of non zero distinct integer solutions of the equation under the above equation are obtained. A few interesting relations between the integral solutions and the special numbers namely Polygonal numbers, Star number, Pronic number and Gnomonic number are exhibited.
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