{"title":"三个二次多项式的和a的n次方,n = (2,3,4,5,6,7,8 & 9)","authors":"S. Tomita, Oliver Couto","doi":"10.13189/ujam.2016.040103","DOIUrl":null,"url":null,"abstract":"Consider the below mentioned equation: x4+y4+z4=w∗tn----(A). Historically Leonard Euler has given parametric solution for equation (A) when w=1 (Ref. no. 9) and degree ‘n'=2. Also S. Realis has given parametric solution for equation (A) when ‘w' equals 1 and degree ‘n' =3. More examples can be found in math literature (Ref. no.6). As is known that solving Diophantine equations for degree greater than four is difficult and the novelty of this paper is that we have done a systematic approach and has provided parametric solutions for degree's ‘n' = (2,3,4,5,6,7,8 & 9 ) for different values of 'w'. The paper is divided into sections (A to H) for degrees (2 to 9) respectively. x4+y4+z4=w∗tn--- (A)","PeriodicalId":372283,"journal":{"name":"Universal Journal of Applied Mathematics","volume":"198 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sum of Three Biquadatics a Multiple of a n th Power, n = (2,3,4,5,6,7,8 & 9)\",\"authors\":\"S. Tomita, Oliver Couto\",\"doi\":\"10.13189/ujam.2016.040103\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Consider the below mentioned equation: x4+y4+z4=w∗tn----(A). Historically Leonard Euler has given parametric solution for equation (A) when w=1 (Ref. no. 9) and degree ‘n'=2. Also S. Realis has given parametric solution for equation (A) when ‘w' equals 1 and degree ‘n' =3. More examples can be found in math literature (Ref. no.6). As is known that solving Diophantine equations for degree greater than four is difficult and the novelty of this paper is that we have done a systematic approach and has provided parametric solutions for degree's ‘n' = (2,3,4,5,6,7,8 & 9 ) for different values of 'w'. The paper is divided into sections (A to H) for degrees (2 to 9) respectively. x4+y4+z4=w∗tn--- (A)\",\"PeriodicalId\":372283,\"journal\":{\"name\":\"Universal Journal of Applied Mathematics\",\"volume\":\"198 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Universal Journal of Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.13189/ujam.2016.040103\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Universal Journal of Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13189/ujam.2016.040103","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Sum of Three Biquadatics a Multiple of a n th Power, n = (2,3,4,5,6,7,8 & 9)
Consider the below mentioned equation: x4+y4+z4=w∗tn----(A). Historically Leonard Euler has given parametric solution for equation (A) when w=1 (Ref. no. 9) and degree ‘n'=2. Also S. Realis has given parametric solution for equation (A) when ‘w' equals 1 and degree ‘n' =3. More examples can be found in math literature (Ref. no.6). As is known that solving Diophantine equations for degree greater than four is difficult and the novelty of this paper is that we have done a systematic approach and has provided parametric solutions for degree's ‘n' = (2,3,4,5,6,7,8 & 9 ) for different values of 'w'. The paper is divided into sections (A to H) for degrees (2 to 9) respectively. x4+y4+z4=w∗tn--- (A)