{"title":"丢番图方程x^2+8∙7^b=y^2r的推广","authors":"S. H. Sapar, Kai Siong Yow","doi":"10.22452/mjs.vol40no2.3","DOIUrl":null,"url":null,"abstract":"We investigate the integral solutions to the Diophantine equation where . We first generalise the forms of and that satisfy the equation. We then show the general forms of non-negative integral solutions to the equation under several conditions. We also investigate some special cases in which the integral solutions exist.","PeriodicalId":18094,"journal":{"name":"Malaysian journal of science","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A GENERALISATION OF THE DIOPHANTINE EQUATION x^2+8∙7^b=y^2r\",\"authors\":\"S. H. Sapar, Kai Siong Yow\",\"doi\":\"10.22452/mjs.vol40no2.3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the integral solutions to the Diophantine equation where . We first generalise the forms of and that satisfy the equation. We then show the general forms of non-negative integral solutions to the equation under several conditions. We also investigate some special cases in which the integral solutions exist.\",\"PeriodicalId\":18094,\"journal\":{\"name\":\"Malaysian journal of science\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Malaysian journal of science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22452/mjs.vol40no2.3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Multidisciplinary\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Malaysian journal of science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22452/mjs.vol40no2.3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Multidisciplinary","Score":null,"Total":0}
A GENERALISATION OF THE DIOPHANTINE EQUATION x^2+8∙7^b=y^2r
We investigate the integral solutions to the Diophantine equation where . We first generalise the forms of and that satisfy the equation. We then show the general forms of non-negative integral solutions to the equation under several conditions. We also investigate some special cases in which the integral solutions exist.