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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Language: | English |
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Wiley
2013-01-01
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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. |
format | Article |
id | doaj-art-4adf4cb430df45018b07e8b79a9f043f |
institution | Kabale University |
issn | 1085-3375 1687-0409 |
language | English |
publishDate | 2013-01-01 |
publisher | Wiley |
record_format | Article |
series | Abstract and Applied Analysis |
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 |