ON THE DIOPHANTINEEQUATION 3^x-p^y=z^2 WHERE p IS PRIME
Keywords:
Diophantine equation, Mihailescu’s Theorem, Non-negative integer solutionAbstract
In this paper, we show that =
is a unique non-negative integer solution of the Diophantine equation
where
is prime and
are non-negative integers satisfying some conditions. For the case
, we give all non-negative integer solutions of this equation.
References
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สุธน ตาดี, และ นภาลัย เหล่ามะลอ. สมการไดโอแฟนไทน n^x-n^y=z^2 และ 2^x-p^y=z^2. วารสารวิจัยราชภัฎพระนคร สาขาวิทยาศาสตร์และเทคโนโลยี, 17(1), 10-16.
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Thongnak, S., Chuayjan, W., & Kaewong, T. (2022). Short communication on the Diophantine equation 7^x-2^y=z^2 where x,y and z are non-negative integers. Annals of Pure and Applied Mathematics, 25(2), 63-66. doi: 10.22457/apam.v25n2a01862
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