Results 1 to 10 of about 120 (115)
The Exponential Diophantine Equation 2x+by=cz [PDF]
The Scientific World Journal, 2014 Let b and c be fixed coprime odd positive integers with min{b,c}>1. In this paper, a classification of all positive integer solutions (x,y,z) of the equation 2x+by=cz is given. Further, by an elementary approach, we prove that if c=b+2, then the equation
Yahui Yu, Xiaoxue Li
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On special exponential Diophantine equations [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we will focus on the study of a special type of exponential Diophantine equations, including a proof. The main contribution of this article is the mentioned type of equations, which can only be solved by the methods of elementary ...
Tomáš Riemel
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The formal solutions of Diophantine equation agy = bx + c [PDF]
HeliyonWe develop a novel method to completely solve the 3-term partial exponential Diophantine equation that represents a generalization of the standard discrete logarithm problem.
Xiazhou Yang
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The Diophantine Equation 8x+py=z2 [PDF]
The Scientific World Journal, 2015 Let p be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i) if p≡±3(mod 8), then the equation 8x+py=z2 has no positive integer solutions (x,y,z); (ii) if p≡7(mod 8), then the equation has only the solutions
Lan Qi, Xiaoxue Li
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On the solution of the exponential Diophantine equation 2x+m2y=z2, for any positive integer m [PDF]
Journal of Hyperstructures, 2023 It is well known that the exponential Diophantine equation 2x+ 1=z2 has the unique solution x=3 and z=3 innon-negative integers, which is closely related to the Catlan's conjecture.
Mridul Dutta, Padma Bhushan Borah
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On perfect powers in $k$-generalized Pell sequence [PDF]
Mathematica Bohemica, 2023 Let $k\geq2$ and let $(P_n^{(k)})_{n\geq2-k}$ be the $k$-generalized Pell sequence defined by \begin{equation*} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)} \end{equation*}for $n\geq2$ with initial conditions \begin{equation*} P_{-(k-2)}^{(
Zafer Şiar +2 more
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On the exponential Diophantine equation mx+(m+1)y=(1+m+m2)z
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Let m > 1 be a positive integer. We show that the exponential Diophantine equation mx + (m + 1)y = (1 + m + m2)z has only the positive integer solution (x, y, z) = (2, 1, 1) when m ≥ 2.
Alan Murat
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Mathematics, 2021 Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In 2016, a research article, entitled – ’power values of sums of products of consecutive integers’, primarily proved the inequality n= 19,736 to obtain all ...
S. Subburam +6 more
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A note on the ternary Diophantine equation x2 − y2m = zn
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Let ℕ be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special cases of the ternary equation x2 − y2m = zn, x, y, z, m, n ∈ ℕ, gcd(x, y) = 1, m ≥ 2, n ≥ 3.
Bérczes Attila +3 more
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Two exponential Diophantine equations [PDF]
Glasgow Mathematical Journal, 1997 In [3], two open problems were whether either of the diophantine equationswith n ∈ Z and f a prime number, is solvable if ω > 3 and 3 √ ω, but in this paper we allow f to be any (rational) integer and also 3 | ω. Equations of this form and more general ones can effectively be solved [5] with an advanced method based on analytical results, but the ...
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