Results 141 to 150 of about 92,931 (194)

On the Exponential Diophantine Equation 29^x+28^y=z^2

International Journal of Mathematical and Computer Sciences
We first show the condition for which the Diophantine equation w^x+(w-1)^y=z^2, where w is a positive integer of the form 24N+5, may admit nonnegative integer solutions.
W. Gayo
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An exponential Diophantine equation x2 + 3a 73b = yn

Journal of Discrete Mathematical Sciences and Cryptography
This paper aims to identify all solutions in positive integers x and y (where x, y ≥ 1), with nonnegative exponents a and b, and an integer n ≥ 3, that satisfy the Diophantine equation x2 + 3a 73b = yn under the condition x and y are coprime.
S. Muthuvel, R. Venkatraman
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Solution of Exponential Diophantine Equation Involving Fermat Primes

International Journal for Research in Applied Science and Engineering Technology
This paper investigates the solutions of specific exponential Diophantine equations involving Fermat primes. Through a structured case-by-case analysis, integer solutions are identified for equations of the form 2 a b z x y   , where x, y,z are non ...
C. Saranya
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A purely exponential Diophantine equation in three unknowns

Periodica Mathematica Hungarica, 2021
The authors consider the exponential equation \[(1)\;\;\; a^x+(ab+1)^y=b^z\ \ \text{in } x,y,z\in\mathbb{Z}_{>0},\] where \(a,b\) are integers \(>1\). They give a list of various pairs \((a,b)\) for which (1) is solvable. This list consists of a couple of infinite families and a finite number of isolated cases. With the exception of two of the infinite
Takafumi Miyazaki, Masaki Sudo, Nobuhiro Terai   +2 more
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On the Exponential Diophantine Equation 9(5^x) - p^y = z^4

International Journal of Mathematical and Computer Sciences
In this article, we determine all solutions to the equation of the form 9(5^x )-p^y=z^4, where p is a prime number and x, y, z are nonnegative integers.
A. Karnbanjong, Kantinan Senin, Supamit Wiriyakulopast, P. Rattanawong   +3 more
semanticscholar   +1 more source

Exponential Diophantine Equations

1986
This is a integrated presentation of the theory of exponential diophantine equations. The authors present, in a clear and unified fashion, applications to exponential diophantine equations and linear recurrence sequences of the Gelfond-Baker theory of linear forms in logarithms of algebraic numbers.
T. N. Shorey, R. Tijdeman
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TERAI'S CONJECTURE ON EXPONENTIAL DIOPHANTINE EQUATIONS

International Journal of Number Theory, 2011
Let a, b, c be relatively prime positive integers such that ap + bq = cr with fixed integers p, q, r ≥ 2. Terai conjectured that the equation ax + by = cz has no positive integral solutions other than (x, y, z) = (p, q, r) except for specific cases. Most known results on this conjecture concern the case where p = q = 2 and either r = 2 or odd r ≥3. In
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On the Exponential Diophantine Equation 2^x-99^y=z^2

International Journal of Latest Technology in Engineering Management & Applied Science
: 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 ...
Wariam Chuayjan, Theeradach Kaewong, Sutthiwat Thongnak   +2 more
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On the exponential Diophantine equation 2x + ny = z2

AIP Conference Proceedings
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S. Thongnak, W. Chuayjan, T. Kaewong
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A Pure Exponential Diophantine Equation

Bulletin of Pure & Applied Sciences- Mathematics and Statistics, 2016
Let u be an even integer. In this paper we prove that if 4| u and u ≥208, then the equation (u3-3u)x + (3u2-1)y = (u2 +1)z has only the positive integer solution (x, y, z) = (2, 2, 3). This result basically determine all solutions of the equation.
Zhong Li, Wei-xun Li
openaire   +1 more source