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Solutions for a Class of the Exponential Diophantine Equation
Advanced Materials Research, 2013We studied the Diophantine equation x2+4n=y11. By using the elementary method and algebraic number theory, we obtain the following conclusions: (i) Let x be an odd number, one necessary condition which the equation has integer solutions is that 210n-1/11 contains some square factors.
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On the exponential Diophantine equation Pm2
This study investigates numbers that are powers of two and can be expressed as the sum of the squares of any two Pell numbers. We apply Baker's theory of linear forms in logarithms of algebraic numbers, along with a variation of the Baker-Davenport reduction method, to solve the Diophantine equation P-m(2) + P-n(2) = 2a, where m,n, and a are non ...Emin, Ahmet, Ates, Firat
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On Two Classes of Exponential Diophantine Equations
Communications in Mathematics and Applications, 2022Padma Bhushan Borah, Mridul Dutta
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Upper bounds for solutions of an exponential Diophantine equation
Rocky Mountain Journal of Mathematics, 2015Takafumi Miyazaki
exaly
On the Exponential Diophantine Equation $$(m^2+m+1)^x+m^y=(m+1)^z $$
Mediterranean Journal of Mathematics, 2020Murat Alan
exaly
A Hasse-type principle for exponential Diophantine equations over number fields and its applications
Monatshefte Fur Mathematik, 2018Csanad Bertok, Lajos Hajdu
exaly
Exponential diophantine equations with four terms. II
1994The reviewer of this paper was also the reviewer of the first part of it [the author and \textit{R. Tijdeman}, Indag. Math., New Ser. 3, No. 1, 47-57 (1992; Zbl 0765.11018)], written in English. But he cannot read Chinese, so he is only able to paraphrase the English summary and to give some further information taken from the international mathematical
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