A method of finding an integral solution to x3 + y3 = kz4
In this article, we proved that an integral solution (a, b, c) to the equation x3+y3 = kz4 is of the form a = rs, b = rt for any two integers s, t and c = (r3u/d3)1/4 for some u with (k,r) = d where k divides a3 + b3 and r is a common factor of a and b.
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
American Institute of Physics
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57284/ http://psasir.upm.edu.my/id/eprint/57284/1/A%20method%20of%20finding%20an%20integral%20solution%20to%20x3%20%2B%20y3%20%3D%20kz4.pdf |
| _version_ | 1848853322568564736 |
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| author | Zahari, N. M. Sapar, Siti Hasana Mohd Atan, Kamel Ariffin |
| author_facet | Zahari, N. M. Sapar, Siti Hasana Mohd Atan, Kamel Ariffin |
| author_sort | Zahari, N. M. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this article, we proved that an integral solution (a, b, c) to the equation x3+y3 = kz4 is of the form a = rs, b = rt for any two integers s, t and c = (r3u/d3)1/4 for some u with (k,r) = d where k divides a3 + b3 and r is a common factor of a and b. |
| first_indexed | 2025-11-15T10:52:08Z |
| format | Conference or Workshop Item |
| id | upm-57284 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:52:08Z |
| publishDate | 2010 |
| publisher | American Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-572842017-09-26T03:59:00Z http://psasir.upm.edu.my/id/eprint/57284/ A method of finding an integral solution to x3 + y3 = kz4 Zahari, N. M. Sapar, Siti Hasana Mohd Atan, Kamel Ariffin In this article, we proved that an integral solution (a, b, c) to the equation x3+y3 = kz4 is of the form a = rs, b = rt for any two integers s, t and c = (r3u/d3)1/4 for some u with (k,r) = d where k divides a3 + b3 and r is a common factor of a and b. American Institute of Physics 2010 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57284/1/A%20method%20of%20finding%20an%20integral%20solution%20to%20x3%20%2B%20y3%20%3D%20kz4.pdf Zahari, N. M. and Sapar, Siti Hasana and Mohd Atan, Kamel Ariffin (2010) A method of finding an integral solution to x3 + y3 = kz4. In: International Conference on Mathematical Science (ICMS), 23-27 Nov. 2010, Bolu, Turkey. (pp. 842-845). 10.1063/1.3525216 |
| spellingShingle | Zahari, N. M. Sapar, Siti Hasana Mohd Atan, Kamel Ariffin A method of finding an integral solution to x3 + y3 = kz4 |
| title | A method of finding an integral solution to x3 + y3 = kz4 |
| title_full | A method of finding an integral solution to x3 + y3 = kz4 |
| title_fullStr | A method of finding an integral solution to x3 + y3 = kz4 |
| title_full_unstemmed | A method of finding an integral solution to x3 + y3 = kz4 |
| title_short | A method of finding an integral solution to x3 + y3 = kz4 |
| title_sort | method of finding an integral solution to x3 + y3 = kz4 |
| url | http://psasir.upm.edu.my/id/eprint/57284/ http://psasir.upm.edu.my/id/eprint/57284/ http://psasir.upm.edu.my/id/eprint/57284/1/A%20method%20of%20finding%20an%20integral%20solution%20to%20x3%20%2B%20y3%20%3D%20kz4.pdf |