{"title":"On a sum of squares of integers in arithmetic progression","authors":"Abdullah Al Kafi Majumdar","doi":"10.3329/jbas.v45i2.57321","DOIUrl":null,"url":null,"abstract":"This paper derives the conditions under which the sum of squares of (2N+1) natural numbers in the arithmetic progression is a perfect square. It is shown that the problem leads to a Diophantine equation, which in turn indicates that there is, in fact, an infinite number of such numbers. Some particular cases are investigated.\nJ. Bangladesh Acad. Sci. 45(2); 241-250: December 2021","PeriodicalId":15109,"journal":{"name":"Journal of Bangladesh Academy of Sciences","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Bangladesh Academy of Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3329/jbas.v45i2.57321","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
This paper derives the conditions under which the sum of squares of (2N+1) natural numbers in the arithmetic progression is a perfect square. It is shown that the problem leads to a Diophantine equation, which in turn indicates that there is, in fact, an infinite number of such numbers. Some particular cases are investigated.
J. Bangladesh Acad. Sci. 45(2); 241-250: December 2021
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