{"title":"数论中的两个主题:能整除n的最大无k数和合数和素数的公式","authors":"R. Jakimczuk","doi":"10.56947/gjom.v14i1.1089","DOIUrl":null,"url":null,"abstract":"In the first part we study the greatest k-free number that divides n. Consequently, we generalize the kernel of the positive integer n. That is, the greatest square-free number that divides n. In the second part we obtain formulas for composite and prime numbers and prove some inequalities.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two topics in number theory: the greatest k-free number that divides n and formulas for composite and prime numbers\",\"authors\":\"R. Jakimczuk\",\"doi\":\"10.56947/gjom.v14i1.1089\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the first part we study the greatest k-free number that divides n. Consequently, we generalize the kernel of the positive integer n. That is, the greatest square-free number that divides n. In the second part we obtain formulas for composite and prime numbers and prove some inequalities.\",\"PeriodicalId\":421614,\"journal\":{\"name\":\"Gulf Journal of Mathematics\",\"volume\":\"34 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-12\",\"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.v14i1.1089\",\"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.v14i1.1089","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Two topics in number theory: the greatest k-free number that divides n and formulas for composite and prime numbers
In the first part we study the greatest k-free number that divides n. Consequently, we generalize the kernel of the positive integer n. That is, the greatest square-free number that divides n. In the second part we obtain formulas for composite and prime numbers and prove some inequalities.
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