Simultaneous pell equations x²-my² = 1 and y²-pz² = 1
Pell equation is a special type of Diophantine equations of the form x²−my²= 1, where m is a positive non-square integer. Since m is not a perfect square, then there exist infinitely many integer solutions(x, y)to the Pell equation. This paper will discuss the integral solutions to the simultaneous...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Institute for Mathematical Research, Universiti Putra Malaysia
2017
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| Online Access: | http://psasir.upm.edu.my/id/eprint/63224/1/Simultaneous%20pell%20equations%20x%C2%B2-my%C2%B2%20%3D%201%20and%20y%C2%B2-pz%C2%B2%20%3D%201.pdf http://psasir.upm.edu.my/id/eprint/63224/ http://einspem.upm.edu.my/journal |
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| Summary: | Pell equation is a special type of Diophantine equations of the form x²−my²= 1, where m is a positive non-square integer. Since m is not a perfect square, then there exist infinitely many integer solutions(x, y)to the Pell equation. This paper will discuss the integral solutions to the simultaneous Pell equationsx²−my²= 1 and y²−pz²= 1, where m is square free integer and p is odd prime. The solutions of these simultaneous equations are of the form of(x, y, z, m) = (yn²t±1, yn, zn, yn²t²±2t)and(y²n/²t±1, yn, zn, y²n/4t²±t) for yn odd and even respectively, where t ∈ N. |
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