Results 11 to 20 of about 92,931 (194)

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]

Heliyon
We 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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Cryptanalysis of some nonabelian group-based key exchange protocols [PDF]

Journal of Mathematical Cryptology
In the recently emerging field of nonabelian group-based cryptography, a prominently used one-way function is the conjugacy search problem (CSP), and two important classes of platform groups are polycyclic and matrix groups. In this paper, we discuss the
Tinani Simran, Matteotti Carlo, Rosenthal Joachim   +2 more
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On the Ternary Exponential Diophantine Equation Equating a Perfect Power and Sum of Products of Consecutive Integers

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, Lewis Nkenyereye, N. Anbazhagan, S. Amutha, M. Kameswari, Woong Cho, Gyanendra Prasad Joshi   +6 more
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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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Solution of the Exponential Diophantine Equation

Journal of Chemical, Biological and physical sciences

semanticscholar   +2 more sources

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, Refik Keskin, Elif Segah Öztaş   +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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