The Experts below are selected from a list of 11475 Experts worldwide ranked by ideXlab platform
Alain Togbé - One of the best experts on this subject based on the ideXlab platform.
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On the Diophantine Equation $$\sum_{j=1}^{k}jP_j^p=P_n^q$$∑j=1kjPjp=Pnq
Acta Mathematica Hungarica, 2020Co-Authors: E Tchammou, Alain TogbéAbstract:We find all the solutions of the title Diophantine Equation $$P_1^p+2P_2^p + \cdots +kP_k^p=P_n^q$$ P 1 p + 2 P 2 p + ⋯ + k P k p = P n q in positive integer variables $$(k, n)$$ ( k , n ) , where $$P_i$$ P i is the $$i^{th}$$ i th term of the Pell sequence if the exponents p, q are included in the set $$\{1,2\}$$ { 1 , 2 } .
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on the Diophantine Equation sum_ j 1 k jp_j p p_n q j 1kjpjp pnq
Acta Mathematica Hungarica, 2020Co-Authors: E Tchammou, Alain TogbéAbstract:We find all the solutions of the title Diophantine Equation $$P_1^p+2P_2^p + \cdots +kP_k^p=P_n^q$$ in positive integer variables $$(k, n)$$, where $$P_i$$ is the $$i^{th}$$ term of the Pell sequence if the exponents p, q are included in the set $$\{1,2\}$$.
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on the exponential Diophantine Equation p_n x p_ n 1 x p_m
Turkish Journal of Mathematics, 2019Co-Authors: Salah Eddine Rihane, Florian Luca, Bernadette Faye, Alain TogbéAbstract:In this paper, we find all the solutions of the title Diophantine Equation in nonnegative integer variables $(m, n, x)$, where $P_k$ is the $k$th term of the Pell sequence.
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on the Diophantine Equation y p frac f x g x
Acta Mathematica Hungarica, 2019Co-Authors: S Subburam, Alain TogbéAbstract:We consider the Diophantine Equation $$y^{p} = \frac{f(x)}{g(x)},$$ where \({x \in \mathbb{Z}}\) and \({y \in \mathbb{Q}}\) are unknowns, f(x) and g(x) are non-zero integer polynomials in variable x and p is prime. We give bounds for x, when \({(x, y) \in \mathbb{Z} \times \mathbb{Q}}\) is a solution of the Equation. This improves the results of some recent papers.
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an exponential Diophantine Equation related to the difference between powers of two consecutive balancing numbers
arXiv: Number Theory, 2018Co-Authors: Salah Eddine Rihane, Florian Luca, Bernadette Faye, Alain TogbéAbstract:In this paper, we find all solutions of the exponential Diophantine Equation $B_{n+1}^x-B_n^x=B_m$ in positive integer variables $(m, n, x)$, where $B_k$ is the $k$-th term of the Balancing sequence.
Florian Luca - One of the best experts on this subject based on the ideXlab platform.
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On a Diophantine Equation involving powers of Fibonacci numbers
'Project Euclid', 2020Co-Authors: Gueth Krisztián, Florian Luca, Szalay LászlóAbstract:This paper deals with the Diophantine Equation F-1(p) + 2F(2)(p )+ . . . + kF(k)(p) = F-n(q), an Equation on the weighted power terms of Fibonacci sequence. For the exponents p, q is an element of {1, 2} the problem has already been solved in ad hoc ways using the properties of the summatory identities appear on the left-hand side of the Equation. Here we suggest a uniform treatment for arbitrary positive integers p and q which works, in practice, for small values. We obtained all the solutions for p, q
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on the exponential Diophantine Equation p_n x p_ n 1 x p_m
Turkish Journal of Mathematics, 2019Co-Authors: Salah Eddine Rihane, Florian Luca, Bernadette Faye, Alain TogbéAbstract:In this paper, we find all the solutions of the title Diophantine Equation in nonnegative integer variables $(m, n, x)$, where $P_k$ is the $k$th term of the Pell sequence.
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an exponential Diophantine Equation related to the difference between powers of two consecutive balancing numbers
arXiv: Number Theory, 2018Co-Authors: Salah Eddine Rihane, Florian Luca, Bernadette Faye, Alain TogbéAbstract:In this paper, we find all solutions of the exponential Diophantine Equation $B_{n+1}^x-B_n^x=B_m$ in positive integer variables $(m, n, x)$, where $B_k$ is the $k$-th term of the Balancing sequence.
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on the Diophantine Equation fn fm 2a
Quaestiones Mathematicae, 2016Co-Authors: Jhon J Bravo, Florian LucaAbstract:AbstractIn this paper, we find all the solutions of the title Diophantine Equation in positive integer variables (n, m, a), where Fk is the kth term of the Fibonacci sequence. The proof of our main theorem uses lower bounds for linear forms in logarithms (Baker's theory) and a version of the Baker-Davenport reduction method in Diophantine approximation.
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on the Diophantine Equation x 2 2 a 3 b 11 c y n
Mathematica Slovaca, 2013Co-Authors: Ismail Naci Cangul, Florian Luca, Musa Demirci, Ilker Inam, Gokhan SoydanAbstract:In this note, we find all the solutions of the Diophantine Equation x2 + 2a · 3b · 11c = yn, in nonnegative integers a, b, c, x, y, n ≥ 3 with x and y coprime.
Arjen K Lenstra - One of the best experts on this subject based on the ideXlab platform.
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solving a linear Diophantine Equation with lower and upper bounds on the variables
Integer Programming and Combinatorial Optimization, 1998Co-Authors: Karen Aardal, Cor Cor Hurkens, Arjen K LenstraAbstract:We develop an algorithm for solving a linear Diophantine Equation with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction, and first finds short vectors satisfying the Diophantine Equation. The next step is to branch on linear combi- nations of these vectors, which either yields a vector that satisfies the bound constraints or provides a proof that no such vector exists. The research was motivated by the need for solving constrained linear dio- phantine Equations as subproblems when designing integrated circuits for video signal processing. Our algorithm is tested with good result on real-life data.
Zhongfeng Zhang - One of the best experts on this subject based on the ideXlab platform.
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on the Diophantine Equation x d 4 x4 x d 4 yn
International Journal of Number Theory, 2017Co-Authors: Zhongfeng ZhangAbstract:In this paper, we study the Diophantine Equation (x − d)4 + x4 + (x + d)4 = yn, and based on Frey–Hellegouarch curves and their corresponding Galois representations, we solve the Equation for various choices of d.
F Sukono - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear Diophantine Equation 11 x +13 y = z 2
IOP Conference Series: Materials Science and Engineering, 2018Co-Authors: A Sugandha, A Tripena, A Prabowo, F SukonoAbstract:This research aims to obtaining the solutions (if any) from the Non Linear Diophantine Equation of 11 x + 13 y = z 2. There are 3 possibilities to obtain the solutions (if any) from the Non Linear Diophantine Equation, namely single, multiple, and no solution. This research is conducted in two stages: (1) by utilizing simulation to obtain the solutions (if any) from the Non Linear Diophantine Equation of 11 x + 13 y = z 2 and (2) by utilizing congruency theory with its characteristics proven that the Non Linear Diophantine Equation has no solution for non negative whole numbers (integers) of x, y, z.
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nonlinear Diophantine Equation 11 x 13 y z 2
IOP Conference Series: Materials Science and Engineering, 2018Co-Authors: A Sugandha, A Tripena, A Prabowo, F SukonoAbstract:This research aims to obtaining the solutions (if any) from the Non Linear Diophantine Equation of 11 x + 13 y = z 2. There are 3 possibilities to obtain the solutions (if any) from the Non Linear Diophantine Equation, namely single, multiple, and no solution. This research is conducted in two stages: (1) by utilizing simulation to obtain the solutions (if any) from the Non Linear Diophantine Equation of 11 x + 13 y = z 2 and (2) by utilizing congruency theory with its characteristics proven that the Non Linear Diophantine Equation has no solution for non negative whole numbers (integers) of x, y, z.
