Results 1 to 10 of about 147 (145)
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 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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Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 Building on theoretical insights and rich experimental data of our preprints, we present here new theoretical and experimental results in three interrelated approaches to the Collatz problem and its generalizations: \emphalgorithmic decidability, random ...
Edward G. Belaga, Maurice Mignotte
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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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An exponential diophantine equation [PDF]
Bulletin of the Australian Mathematical Society, 2001 Let p be an odd prime with p > 3. In this paper we give all positive integer solutions (x, y, m, n) of the equation x2 + p2m = yn, gcd (x, y) = 1, n > 2 satisfying 2 | n of 2 ∤ n and p ≢ (−1)(p−1)/2(mod 4n.
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Two exponential diophantine equations [PDF]
Journal de théorie des nombres de Bordeaux, 2017 The equation 3 a +5 b -7 c =1, to be solved in non-negative rational integers a,b,c, has been mentioned by Masser as an example for which there is still no algorithm to solve completely. Despite this, we find here all the solutions. The equation y 2 =3 a +2 b +1, to be solved in non-negative rational integers a,b and a rational integer y, has been ...
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