{"title":"丢番图方程\\美元压裂{1}{x} + \\压裂{3}{y} + \\压裂{5}{z} = \\压裂{3}{4}}$","authors":"Hunar Sherzad Taher","doi":"10.37418/amsj.12.1.4","DOIUrl":null,"url":null,"abstract":"In this paper, we show that the Diophantine equation $\\frac{1}{x}+\\frac{3}{y}+\\frac{5}{z}=\\frac{3}{4}$ has finitely many integral solutions in the positive integers $x,y$ and $z$.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"418 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON THE DIOPHANTINE EQUATION $\\\\frac{1}{x}+\\\\frac{3}{y}+\\\\frac{5}{z}=\\\\frac{3}{4}}$\",\"authors\":\"Hunar Sherzad Taher\",\"doi\":\"10.37418/amsj.12.1.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we show that the Diophantine equation $\\\\frac{1}{x}+\\\\frac{3}{y}+\\\\frac{5}{z}=\\\\frac{3}{4}$ has finitely many integral solutions in the positive integers $x,y$ and $z$.\",\"PeriodicalId\":231117,\"journal\":{\"name\":\"Advances in Mathematics: Scientific Journal\",\"volume\":\"418 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics: Scientific Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37418/amsj.12.1.4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics: Scientific Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37418/amsj.12.1.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ON THE DIOPHANTINE EQUATION $\frac{1}{x}+\frac{3}{y}+\frac{5}{z}=\frac{3}{4}}$
In this paper, we show that the Diophantine equation $\frac{1}{x}+\frac{3}{y}+\frac{5}{z}=\frac{3}{4}$ has finitely many integral solutions in the positive integers $x,y$ and $z$.
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