On The Diophantine Equation 2^x + p^y = z^2 where x ≠ 1 and p ≡ 3 (mod 4)

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Published: Aug 30, 2022
Keywords:
Diophantine equation, Catalan’s conjecture

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Suton Tadee
Department of Mathematics, Faculty of Science and Technology, Thepsatri Rajabhat University, Lopburi 15000

Abstract

In this paper, we show that all non-negative integer solutions of the Diophantine equation gif.latex?2^x&space;+&space;p^y&space;=z^2, where gif.latex?x\neq&space;1,~p is prime and gif.latex?p&space;\equiv&space;3\pmod&space;4, are


gif.latex?(x,p,y,z)\in\{(3,p,0,3)\}\cup&space;\{(0,3,1,2)\}\cup\\&space;~~~~~~~~~~~~~~~~~~~~~~&space;\{(2+\log_2&space;(p+1),p,2,p+2):\log_2(p+1)\in\mathbb{Z}\}

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How to Cite
Tadee, S. (2022). On The Diophantine Equation 2^x + p^y = z^2 where x ≠ 1 and p ≡ 3 (mod 4). Mathematical Journal by The Mathematical Association of Thailand Under The Patronage of His Majesty The King, 67(707), 13–19. Retrieved from https://ph02.tci-thaijo.org/index.php/MJMATh/article/view/246046
Issue
Vol. 67 No. 707 (2022): May – August 2022
Section
Research Article

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