Graceful numbers
We construct a labeled graph D(n) that reflects the structure of divisors of a given natural number n. We define the concept of graceful numbers in terms of this associated graph and find the general form of such a number. As a consequence, we determine which graceful numbers are perfect.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007615 |
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| _version_ | 1832555813122605056 |
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| author | Kiran R. Bhutani Alexander B. Levin |
| author_facet | Kiran R. Bhutani Alexander B. Levin |
| author_sort | Kiran R. Bhutani |
| collection | DOAJ |
| description | We construct a labeled graph D(n) that reflects the structure of divisors of a given natural number n. We define the concept of graceful numbers in terms of this associated graph and find the general form of such a number. As a consequence, we determine which graceful numbers are perfect. |
| format | Article |
| id | doaj-art-cd539b37b97b492f997157331b0b6acb |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cd539b37b97b492f997157331b0b6acb2025-02-03T05:47:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0129849549910.1155/S0161171202007615Graceful numbersKiran R. Bhutani0Alexander B. Levin1Department of Mathematics, The Catholic University of America, Washington, DC 20064, USADepartment of Mathematics, The Catholic University of America, Washington, DC 20064, USAWe construct a labeled graph D(n) that reflects the structure of divisors of a given natural number n. We define the concept of graceful numbers in terms of this associated graph and find the general form of such a number. As a consequence, we determine which graceful numbers are perfect.http://dx.doi.org/10.1155/S0161171202007615 |
| spellingShingle | Kiran R. Bhutani Alexander B. Levin Graceful numbers International Journal of Mathematics and Mathematical Sciences |
| title | Graceful numbers |
| title_full | Graceful numbers |
| title_fullStr | Graceful numbers |
| title_full_unstemmed | Graceful numbers |
| title_short | Graceful numbers |
| title_sort | graceful numbers |
| url | http://dx.doi.org/10.1155/S0161171202007615 |
| work_keys_str_mv | AT kiranrbhutani gracefulnumbers AT alexanderblevin gracefulnumbers |