{"title":"费马定理的特例","authors":"L. Gallardo","doi":"10.56947/gjom.v13i2.868","DOIUrl":null,"url":null,"abstract":"We prove under a mild condition that the only rationals x, y with x ≥ 0, y≥ 0 and x+y=N(k), for some k ∈ Q*, and xp+yp=1 are x=0, y=1 and x=1, y=0. Here, we let N denote the norm from Q(ωp) to Q for p an odd prime number.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Special case of Fermat's Theorem\",\"authors\":\"L. Gallardo\",\"doi\":\"10.56947/gjom.v13i2.868\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove under a mild condition that the only rationals x, y with x ≥ 0, y≥ 0 and x+y=N(k), for some k ∈ Q*, and xp+yp=1 are x=0, y=1 and x=1, y=0. Here, we let N denote the norm from Q(ωp) to Q for p an odd prime number.\",\"PeriodicalId\":421614,\"journal\":{\"name\":\"Gulf Journal of Mathematics\",\"volume\":\"49 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Gulf Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56947/gjom.v13i2.868\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gulf Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56947/gjom.v13i2.868","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove under a mild condition that the only rationals x, y with x ≥ 0, y≥ 0 and x+y=N(k), for some k ∈ Q*, and xp+yp=1 are x=0, y=1 and x=1, y=0. Here, we let N denote the norm from Q(ωp) to Q for p an odd prime number.
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