{"title":"关于丢番图方程z2 = k(k2 + 3)和z2 = k(k2 + 12)","authors":"Shah Mohammad Shahidul Islam, A. Majumdar","doi":"10.3329/JBAS.V45I1.54265","DOIUrl":null,"url":null,"abstract":"This paper provides an analytical method of finding all the (positive, integral) solutions of the Diophantine equation z2 = k(k2+3). We also prove analytically that the Diophantine equation z2 = k(k2+12) has no positive, integer solution. \nJ. Bangladesh Acad. Sci. 45(1); 127-129: June 2021","PeriodicalId":15109,"journal":{"name":"Journal of Bangladesh Academy of Sciences","volume":"48 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Diophantine equations z2 = k(k2 + 3) and z2 = k(k2 + 12)\",\"authors\":\"Shah Mohammad Shahidul Islam, A. Majumdar\",\"doi\":\"10.3329/JBAS.V45I1.54265\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper provides an analytical method of finding all the (positive, integral) solutions of the Diophantine equation z2 = k(k2+3). We also prove analytically that the Diophantine equation z2 = k(k2+12) has no positive, integer solution. \\nJ. Bangladesh Acad. Sci. 45(1); 127-129: June 2021\",\"PeriodicalId\":15109,\"journal\":{\"name\":\"Journal of Bangladesh Academy of Sciences\",\"volume\":\"48 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Bangladesh Academy of Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3329/JBAS.V45I1.54265\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Bangladesh Academy of Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3329/JBAS.V45I1.54265","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Diophantine equations z2 = k(k2 + 3) and z2 = k(k2 + 12)
This paper provides an analytical method of finding all the (positive, integral) solutions of the Diophantine equation z2 = k(k2+3). We also prove analytically that the Diophantine equation z2 = k(k2+12) has no positive, integer solution.
J. Bangladesh Acad. Sci. 45(1); 127-129: June 2021
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