{"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}
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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.
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