Note on the Lower Bound of Least Common Multiple

Consider a sequence of positive integers in arithmetic progression with . Denote the least common multiple of by . We show that if , then , and we obtain optimum result on in some cases for such estimate. Besides, for quadratic sequences , we also show that the least common multiple is at least...

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Main Author: Shea-Ming Oon
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/218125
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author Shea-Ming Oon
author_facet Shea-Ming Oon
author_sort Shea-Ming Oon
collection DOAJ
description Consider a sequence of positive integers in arithmetic progression with . Denote the least common multiple of by . We show that if , then , and we obtain optimum result on in some cases for such estimate. Besides, for quadratic sequences , we also show that the least common multiple is at least when , which sharpens a recent result of Farhi.
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spelling doaj-art-4adf4cb430df45018b07e8b79a9f043f2025-02-03T01:31:10ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/218125218125Note on the Lower Bound of Least Common MultipleShea-Ming Oon0Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, MalaysiaConsider a sequence of positive integers in arithmetic progression with . Denote the least common multiple of by . We show that if , then , and we obtain optimum result on in some cases for such estimate. Besides, for quadratic sequences , we also show that the least common multiple is at least when , which sharpens a recent result of Farhi.http://dx.doi.org/10.1155/2013/218125
spellingShingle Shea-Ming Oon
Note on the Lower Bound of Least Common Multiple
Abstract and Applied Analysis
title Note on the Lower Bound of Least Common Multiple
title_full Note on the Lower Bound of Least Common Multiple
title_fullStr Note on the Lower Bound of Least Common Multiple
title_full_unstemmed Note on the Lower Bound of Least Common Multiple
title_short Note on the Lower Bound of Least Common Multiple
title_sort note on the lower bound of least common multiple
url http://dx.doi.org/10.1155/2013/218125
work_keys_str_mv AT sheamingoon noteonthelowerboundofleastcommonmultiple