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On Exponential Diophantine Equation Incorporating Krishnamurthy Numbers
Arya Bhatta Journal of Mathematics and InformaticsG. Janaki, R. Sarulatha
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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 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 a conjecture on exponential Diophantine equations [PDF]
Acta Arithmetica, 2008 We study the solutions of a Diophantine equation of the form $a^x+b^y=c^z$, where $a\equiv 2 \pmod 4$, $b\equiv 3 \pmod 4$ and $\gcd (a,b,c)=1$. The main result is that if there exists a solution $(x,y,z)=(2,2,r)$ with $r>1$ odd then this is the only ...
Cipu, Mihai, Mignotte, Maurice
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Exponential Diophantine equations [PDF]
Pacific Journal of Mathematics, 1982 Brenner, J. L., Foster, Lorraine L.
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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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All Solutions of the Diophantine Equations $2F_{n}=3^{s}⋅y^{b}$ and $F_{n}±1=3^{s}⋅y^{b}$
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2022 The Fibonacci sequence 〖(F〗_n) is defined by F_0=0, F_1=1, and F_n=F_(n-1)+F_(n-2) for n≥2. In this paper, we will give all solutions of the Diophantine equations 2F_n=3^s∙y^b and F_n±1=3^s∙y^b in nonnegative integers s≥0, y≥1, b≥2, n≥1 and (3,y)=1.
İbrahim Erduran, Zafer Şiar
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Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 Let (M_k) be the sequence of Mulatu numbers defined by M_0=4, M_1=1, M_k=M_(k-1)+M_(k-2) and (F_k) be the Fibonacci sequence given by the recurrence F_k=F_(k-1)+F_(k-2) with the initial conditions F_0=0, F_1=1 for k≥2.
Fatih Erduvan, Merve Güney Duman
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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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