{"title":"关于四次丢番图方程的解","authors":"Mokhtar Ahmadi, A. S. Janfada, K. Nabardi","doi":"10.24193/mathcluj.2023.1.02","DOIUrl":null,"url":null,"abstract":"In this article, first, using the elliptic curve method, it is proved that the quartic Diophantine equations x^4-y^4=k(t^lambda-u^4{+-} v^4) for positive even lambda and integers k and t has infinitely many non-trivial rational solutions. Then, by direct ways, parametric solutions for equations x^4-y^4=k(t^3{+-} u^4-v^4) are found.","PeriodicalId":39356,"journal":{"name":"Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the solutions of quartic Diophantine equations\",\"authors\":\"Mokhtar Ahmadi, A. S. Janfada, K. Nabardi\",\"doi\":\"10.24193/mathcluj.2023.1.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, first, using the elliptic curve method, it is proved that the quartic Diophantine equations x^4-y^4=k(t^lambda-u^4{+-} v^4) for positive even lambda and integers k and t has infinitely many non-trivial rational solutions. Then, by direct ways, parametric solutions for equations x^4-y^4=k(t^3{+-} u^4-v^4) are found.\",\"PeriodicalId\":39356,\"journal\":{\"name\":\"Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24193/mathcluj.2023.1.02\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/mathcluj.2023.1.02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
In this article, first, using the elliptic curve method, it is proved that the quartic Diophantine equations x^4-y^4=k(t^lambda-u^4{+-} v^4) for positive even lambda and integers k and t has infinitely many non-trivial rational solutions. Then, by direct ways, parametric solutions for equations x^4-y^4=k(t^3{+-} u^4-v^4) are found.
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