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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| Format: | Article |
| 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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| _version_ | 1832558926127693824 |
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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 |