{"title":"子平衡数","authors":"R. K. Davala, G. Panda","doi":"10.11113/matematika.v34.n1.829","DOIUrl":null,"url":null,"abstract":"A natural number $n$ is called balancing number (with balancer $r$)if it satisfies the Diophantine equation $1+2+\\cdots+(n-1)=(n+1)+(n+2)+\\cdots+(n+r).$ However, if for some pair of natural numbers $(n,r)$, $1+2+\\cdots+(n-1) < (n+1)+(n+2)+\\cdots+(n+r)$ and equality is achieved after adding a natural number $D$ to the left hand side then we call $n$ a $D$-subbalancing number with $D$-subbalaner number $r$. In this paper, such numbers are studied for certain values of $D$.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2018-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Subbalancing Numbers\",\"authors\":\"R. K. Davala, G. Panda\",\"doi\":\"10.11113/matematika.v34.n1.829\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A natural number $n$ is called balancing number (with balancer $r$)if it satisfies the Diophantine equation $1+2+\\\\cdots+(n-1)=(n+1)+(n+2)+\\\\cdots+(n+r).$ However, if for some pair of natural numbers $(n,r)$, $1+2+\\\\cdots+(n-1) < (n+1)+(n+2)+\\\\cdots+(n+r)$ and equality is achieved after adding a natural number $D$ to the left hand side then we call $n$ a $D$-subbalancing number with $D$-subbalaner number $r$. In this paper, such numbers are studied for certain values of $D$.\",\"PeriodicalId\":43733,\"journal\":{\"name\":\"Matematika\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2018-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11113/matematika.v34.n1.829\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11113/matematika.v34.n1.829","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
A natural number $n$ is called balancing number (with balancer $r$)if it satisfies the Diophantine equation $1+2+\cdots+(n-1)=(n+1)+(n+2)+\cdots+(n+r).$ However, if for some pair of natural numbers $(n,r)$, $1+2+\cdots+(n-1) < (n+1)+(n+2)+\cdots+(n+r)$ and equality is achieved after adding a natural number $D$ to the left hand side then we call $n$ a $D$-subbalancing number with $D$-subbalaner number $r$. In this paper, such numbers are studied for certain values of $D$.