{"title":"关于（k，r）-整数基根的分布","authors":"T. Srichan, Pinthira Tangsupphathawat","doi":"10.52737/18291163-2019.11.12-1-12","DOIUrl":null,"url":null,"abstract":"Let $k$ and $r$ be fixed integers with $1<r<k$. A positive integer is called $r$-free if it is not divisible by the $r^{th}$ power of any prime. A positive integer $n$ is called a $(k,r)$-integer if $n$ is written in the form $a^kb$ where $b$ is an $r$-free integer. Let $p$ be an odd prime and let $x>1$ be a real number.\n\nIn this paper an asymptotic formula for the number of $(k,r)$-integers which are primitive roots modulo $p$ and do not exceed $x$ is obtained.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the distribution of primitive roots that are (k,r)-integers\",\"authors\":\"T. Srichan, Pinthira Tangsupphathawat\",\"doi\":\"10.52737/18291163-2019.11.12-1-12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $k$ and $r$ be fixed integers with $1<r<k$. A positive integer is called $r$-free if it is not divisible by the $r^{th}$ power of any prime. A positive integer $n$ is called a $(k,r)$-integer if $n$ is written in the form $a^kb$ where $b$ is an $r$-free integer. Let $p$ be an odd prime and let $x>1$ be a real number.\\n\\nIn this paper an asymptotic formula for the number of $(k,r)$-integers which are primitive roots modulo $p$ and do not exceed $x$ is obtained.\",\"PeriodicalId\":42323,\"journal\":{\"name\":\"Armenian Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2019-12-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Armenian Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.52737/18291163-2019.11.12-1-12\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Armenian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52737/18291163-2019.11.12-1-12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the distribution of primitive roots that are (k,r)-integers
Let $k$ and $r$ be fixed integers with $11$ be a real number.
In this paper an asymptotic formula for the number of $(k,r)$-integers which are primitive roots modulo $p$ and do not exceed $x$ is obtained.
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