On the Exponential Diophantine Equation 2^x-99^y=z^2

Author:

Wariam Chuayjan ,Theeradach Kaewong ,Sutthiwat Thongnak

Abstract

Abstract: In this work, we determine all non-negative integers solution  to the exponential Diophantine equation .  The mathematical process bases on several theorems in Number theory, including the modular arithmetic, Divisibility and the Division Algorithm.  The solution set to the equation is .  

Publisher

RSIS International

Reference8 articles.

1. 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.

2. 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(3) 643-650.

3. 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.

4. Tadee, S., (2022) On the Diophantine equation (p+6)^x-p^y=z^2 where p is a Prime Number, Journal of Mathematics and Informatics, 23 51-54.

5. 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.

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