{"title":"关于两个丢番图方程9x - 3y = z2和13x - 7y = z2的注记","authors":"S. Tadee","doi":"10.22457/jmi.v24a02215","DOIUrl":null,"url":null,"abstract":"In this short note, we show that the Diophantine equation 2 9 3 x y − = z has all non-negative integer solutions , , ∈ { , 2 , 0 : ∈ ℕ ∪ {0}} and the Diophantine equation 2 13 7 x y − = z have the unique non-negative integer solution ( , , ) (0,0,0) x y z = .","PeriodicalId":43016,"journal":{"name":"Journal of Applied Mathematics Statistics and Informatics","volume":"1 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Short Note on Two Diophantine Equations 9 x – 3y = z2 and 13x – 7y = z2\",\"authors\":\"S. Tadee\",\"doi\":\"10.22457/jmi.v24a02215\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this short note, we show that the Diophantine equation 2 9 3 x y − = z has all non-negative integer solutions , , ∈ { , 2 , 0 : ∈ ℕ ∪ {0}} and the Diophantine equation 2 13 7 x y − = z have the unique non-negative integer solution ( , , ) (0,0,0) x y z = .\",\"PeriodicalId\":43016,\"journal\":{\"name\":\"Journal of Applied Mathematics Statistics and Informatics\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mathematics Statistics and Informatics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22457/jmi.v24a02215\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics Statistics and Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22457/jmi.v24a02215","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
在这篇简短的笔记中，我们证明了Diophantine方程2,3 x y−= z有所有的非负整数解，，∈{，2,0:∈∪{0}}，并且Diophantine方程2,7 x y−= z有唯一的非负整数解(，，)(0,0,0)x y z =。
A Short Note on Two Diophantine Equations 9 x – 3y = z2 and 13x – 7y = z2
In this short note, we show that the Diophantine equation 2 9 3 x y − = z has all non-negative integer solutions , , ∈ { , 2 , 0 : ∈ ℕ ∪ {0}} and the Diophantine equation 2 13 7 x y − = z have the unique non-negative integer solution ( , , ) (0,0,0) x y z = .
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