On the Exponential Diophantine Equation 15^x-17^y=z^2
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Keywords

divisibility
exponential Diophantine equation
modular arithmetic
prime number

How to Cite

On the Exponential Diophantine Equation 15^x-17^y=z^2. (2024). International Journal of Latest Technology in Engineering Management & Applied Science, 13(5), 215-217. https://doi.org/10.51583/IJLTEMAS.2024.130522

Abstract

In this work, the exponential Diophantine equation 15x-17y=z2, where x,y and z are non-negative integers, was studied and presented with the theorems governing its expressions. The result indicated that (x,y,z)= (0,0,0) was a unique solution to the equation.

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References

Buosi, M., Lemos, A., Porto, A. L. P. and Santiago, D. F. G., (2020) On the exponential Diophantine equation p^x-2^y=z^2 with p=k^2+2 , a prime number, Southeast-Asian Journal of Sciences, 8(2) 103-109.

Elshahed, A. and Kamarulhaili, H, (2020) On the exponential Diophantine equation (4^n )^x-p^y=z^2 , WSEAS TRANSACTION on MATHEMATICS, 19, 349-352.

Rabago, J. F. T., (2018) On the Diophantine equation 4^x-p^y=3z^2 where p is a Prime, Thai Journal of Mathematics, 16 (2018) 643-650.

Tadee, S., (2023) On the Diophantine equation 3^x-p^y=z^2where p is Prime, Journal of Science and Technology Thonburi University, 7(1), 1-6.

Tadee, S., (2023) A Short Note On two Diophantine equations 9^x-3^y=z^2and 13^x-7^y=z^2, Journal of Mathematics and Informatics, 24, 23-25.

Burton, D. M., (2011) Elementary Number Theory, McGraw-Hill.

Thongnak, S., Chuayjan, W. and Kaewong, T., (2019) On the exponential Diophantine equation 2^x-3^y=z^2, Southeast Asian Journal of Science, 7 (1) 1-4.

Thongnak, S., Chuayjan, W. and Kaewong, T., (2021) The Solution of the Exponential Diophantine Equation 7^x-5^y=z^2, Mathematical Journal, 66 (7) 62-67.

Thongnak, S., Chuayjan, W. and Kaewong, T., (2022) On the Diophantine Equation 7^x-2^y=z^2where x,yand z are Non-Negative Integers, Annals of Pure and Applied Mathematics, 25 (2) 63-66.

Thongnak, S., Chuayjan, W. and Kaewong, T., (2023) On the Diophantine Equation 15^x-13^y=z^2, Annals of Pure and Applied Mathematics, 27(1) 23-26.

Thongnak, S., Kaewong, T. and Chuayjan, W., (2023) On the Diophantine Equation 55^x-53^y=z^2, Annals of Pure and Applied Mathematics, 27(1) 27-300.