Simultaneous Pell equations
This paper will discuss the solutions on the simultaneous Pell equations x2 − my2 = 1 and y2 − 11z2 = 1 where m is square free. By looking at the pattern of the solutions, some theorems will be developed. The solutions to these simultaneous equations are (x, y, z, m) = (50i − 1, 10, 3, mi) and (50i...
| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/57356/1/Simultaneous%20Pell%20equations.pdf |
| _version_ | 1796976675880173568 |
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| author | Sihabudin, Nurul Amirah Sapar, Siti Hasana Mohamad Johari, Mohamad Aidil |
| author_facet | Sihabudin, Nurul Amirah Sapar, Siti Hasana Mohamad Johari, Mohamad Aidil |
| author_sort | Sihabudin, Nurul Amirah |
| collection | UPM |
| description | This paper will discuss the solutions on the simultaneous Pell equations x2 − my2 = 1 and y2 − 11z2 = 1 where m is square free. By looking at the pattern of the solutions, some theorems will be developed. The solutions to these simultaneous equations are (x, y, z, m) = (50i − 1, 10, 3, mi) and (50i + 1, 10, 3, mi) for some expressions of mi where i is natural number. |
| first_indexed | 2024-03-06T09:29:08Z |
| format | Conference or Workshop Item |
| id | upm.eprints-57356 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:29:08Z |
| publishDate | 2015 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | upm.eprints-573562017-09-26T04:09:50Z http://psasir.upm.edu.my/id/eprint/57356/ Simultaneous Pell equations Sihabudin, Nurul Amirah Sapar, Siti Hasana Mohamad Johari, Mohamad Aidil This paper will discuss the solutions on the simultaneous Pell equations x2 − my2 = 1 and y2 − 11z2 = 1 where m is square free. By looking at the pattern of the solutions, some theorems will be developed. The solutions to these simultaneous equations are (x, y, z, m) = (50i − 1, 10, 3, mi) and (50i + 1, 10, 3, mi) for some expressions of mi where i is natural number. AIP Publishing 2015 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/57356/1/Simultaneous%20Pell%20equations.pdf Sihabudin, Nurul Amirah and Sapar, Siti Hasana and Mohamad Johari, Mohamad Aidil (2015) Simultaneous Pell equations. In: 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23), 24-26 Nov. 2015, Johor Bahru, Malaysia. (pp. 1-3). 10.1063/1.4954602 |
| spellingShingle | Sihabudin, Nurul Amirah Sapar, Siti Hasana Mohamad Johari, Mohamad Aidil Simultaneous Pell equations |
| title | Simultaneous Pell equations |
| title_full | Simultaneous Pell equations |
| title_fullStr | Simultaneous Pell equations |
| title_full_unstemmed | Simultaneous Pell equations |
| title_short | Simultaneous Pell equations |
| title_sort | simultaneous pell equations |
| url | http://psasir.upm.edu.my/id/eprint/57356/1/Simultaneous%20Pell%20equations.pdf |
| work_keys_str_mv | AT sihabudinnurulamirah simultaneouspellequations AT saparsitihasana simultaneouspellequations AT mohamadjoharimohamadaidil simultaneouspellequations |