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: | , , |
|---|---|
| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
American Institute of Physics
2010
|
| Online Access: | 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_ | 1825931581979623424 |
|---|---|
| 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. |
| collection | UPM |
| 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 | 2024-03-06T09:28:55Z |
| format | Conference or Workshop Item |
| id | upm.eprints-57284 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:28:55Z |
| publishDate | 2010 |
| publisher | American Institute of Physics |
| record_format | dspace |
| spelling | upm.eprints-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/57284/1/A%20method%20of%20finding%20an%20integral%20solution%20to%20x3%20%2B%20y3%20%3D%20kz4.pdf |
| work_keys_str_mv | AT zaharinm amethodoffindinganintegralsolutiontox3y3kz4 AT saparsitihasana amethodoffindinganintegralsolutiontox3y3kz4 AT mohdatankamelariffin amethodoffindinganintegralsolutiontox3y3kz4 AT zaharinm methodoffindinganintegralsolutiontox3y3kz4 AT saparsitihasana methodoffindinganintegralsolutiontox3y3kz4 AT mohdatankamelariffin methodoffindinganintegralsolutiontox3y3kz4 |