{"title":"一个没有非平凡解的方程组","authors":"H. Gupta","doi":"10.6028/JRES.071B.024","DOIUrl":null,"url":null,"abstract":"L The object of this note is to prove the THEOREM: The system of equations af + a~ + . + a~_1 = br + b~ + . . . + b~_l' r=2,3, .. . , n ; (1) has no nontrivial solutions in positive integers. In what follows, we write Ar for a~+ a;+ \"'\" 1; Br for bi+ b;+ + b~_ I' r\"'\" 1; and all small letters denote integers\"'\" 0 unless stated otherwise. 2. PROOF OF THE THEOREM: Let at, a2, ... , a,,_1 From (4) we have AI 1 0 0 0 A2 AI 2 0 0 A3 A2 AI 3 0 r!'\\r =","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1967-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A system of equations having no nontrivial solutions\",\"authors\":\"H. Gupta\",\"doi\":\"10.6028/JRES.071B.024\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"L The object of this note is to prove the THEOREM: The system of equations af + a~ + . + a~_1 = br + b~ + . . . + b~_l' r=2,3, .. . , n ; (1) has no nontrivial solutions in positive integers. In what follows, we write Ar for a~+ a;+ \\\"'\\\" 1; Br for bi+ b;+ + b~_ I' r\\\"'\\\" 1; and all small letters denote integers\\\"'\\\" 0 unless stated otherwise. 2. PROOF OF THE THEOREM: Let at, a2, ... , a,,_1 From (4) we have AI 1 0 0 0 A2 AI 2 0 0 A3 A2 AI 3 0 r!'\\\\r =\",\"PeriodicalId\":408709,\"journal\":{\"name\":\"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1967-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.6028/JRES.071B.024\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.6028/JRES.071B.024","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A system of equations having no nontrivial solutions
L The object of this note is to prove the THEOREM: The system of equations af + a~ + . + a~_1 = br + b~ + . . . + b~_l' r=2,3, .. . , n ; (1) has no nontrivial solutions in positive integers. In what follows, we write Ar for a~+ a;+ "'" 1; Br for bi+ b;+ + b~_ I' r"'" 1; and all small letters denote integers"'" 0 unless stated otherwise. 2. PROOF OF THE THEOREM: Let at, a2, ... , a,,_1 From (4) we have AI 1 0 0 0 A2 AI 2 0 0 A3 A2 AI 3 0 r!'\r =
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