On the Diophantine Equation 5 x + p mn y = z 2
Diophantine equation is a polynomial equation with two or more unknowns for which only integral solutions are sought. This paper concentrates on finding the integral solutions to the Diophantine equation 5 x + p mn y = z 2 where p > 5 a prime number and y = 1, 2. The positive integral solutions t...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Institute for Mathematical Research, Universiti Putra Malaysia
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/81535/1/Diophantine.pdf http://psasir.upm.edu.my/id/eprint/81535/ https://mjms.upm.edu.my/senaraimakalah.php?yr=2019&bln=April&vol=13(S) |
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| Summary: | Diophantine equation is a polynomial equation with two or more unknowns for which only integral solutions are sought. This paper concentrates on finding the integral solutions to the Diophantine equation 5 x + p mn y = z 2 where p > 5 a prime number and y = 1, 2. The positive integral solutions to the equation are (x, m, n, y, z) = (2r, t, pt k 2 ± 2k5 r , 1, pt k ± 5 r ) and 2r, 2t, 5 2r−α − 5 α 2p t , 2, 5 2r−α + 5α 2 for k, r, t ∈ N where 0 ≤ α < r. |
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