{"title":"关于两次四次方之差","authors":"Nguyen Xuan Tho","doi":"10.1017/s0013091523000706","DOIUrl":null,"url":null,"abstract":"Abstract We investigate the equation $D=x^4-y^4$ in field extensions. As an application, for a prime number p , we find solutions to $p=x^4-y^4$ if $p\\equiv 11$ (mod 16) and $p^3=x^4-y^4$ if $p\\equiv 3$ (mod 16) in all cubic extensions of $\\mathbb{Q}(i)$ .","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":"93 12","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Difference of Two Fourth Powers\",\"authors\":\"Nguyen Xuan Tho\",\"doi\":\"10.1017/s0013091523000706\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We investigate the equation $D=x^4-y^4$ in field extensions. As an application, for a prime number p , we find solutions to $p=x^4-y^4$ if $p\\\\equiv 11$ (mod 16) and $p^3=x^4-y^4$ if $p\\\\equiv 3$ (mod 16) in all cubic extensions of $\\\\mathbb{Q}(i)$ .\",\"PeriodicalId\":20586,\"journal\":{\"name\":\"Proceedings of the Edinburgh Mathematical Society\",\"volume\":\"93 12\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-11-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Edinburgh Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/s0013091523000706\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Edinburgh Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/s0013091523000706","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
研究了域扩展中的方程$D=x^4-y^4$。作为一个应用，对于素数p，我们找到了$p=x^4-y^4$ if $p\equiv 11$ (mod 16)和$p^3=x^4-y^4$ if $p\equiv 3$ (mod 16)在$\mathbb{Q}(i)$的所有三次扩展中的解。
Abstract We investigate the equation $D=x^4-y^4$ in field extensions. As an application, for a prime number p , we find solutions to $p=x^4-y^4$ if $p\equiv 11$ (mod 16) and $p^3=x^4-y^4$ if $p\equiv 3$ (mod 16) in all cubic extensions of $\mathbb{Q}(i)$ .
期刊介绍：
The Edinburgh Mathematical Society was founded in 1883 and over the years, has evolved into the principal society for the promotion of mathematics research in Scotland. The Society has published its Proceedings since 1884. This journal contains research papers on topics in a broad range of pure and applied mathematics, together with a number of topical book reviews.
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