On the exponential Diophantine equation Pxn + Pxn+1 + ⋯ + Pxn+k-1 = Pm
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Florian Luca
Abstract
In this paper, we find all the solutions of the title Diophantine equation in positive integers (m, n, k, x), where Pi is the ith term of the Pell sequence.
Acknowledgement
The authors thank the referees for the useful comments to improve the quality of this paper.
(Communicated by István Gaál
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© 2020 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- Fuzzy deductive systems of RM algebras
- Congruence pairs of principal MS-algebras and perfect extensions
- The lattices of 𝔏-fuzzy state filters in state residuated lattices
- Central lifting property for orthomodular lattices
- EQ-Modules
- On the exponential Diophantine equation Pxn + Pxn+1 + ⋯ + Pxn+k-1 = Pm
- Remarks on some generalization of the notion of microscopic sets
- Disjointness of composition operators on Hv0 spaces
- A common fixed point theorem for non-self mappings in strictly convex menger PM-spaces
- The Poincaré-Cartan forms of one-dimensional variational integrals
- Coarse cohomology with twisted coefficients
- Divisible extension of probability
- Asymptotic behavior of the records of multivariate random sequences in a norm sense
- Strong convergence of the functional nonparametric relative error regression estimator under right censoring
- A new kumaraswamy generalized family of distributions: Properties and applications
- Efficient message transmission via twisted Edwards curves
- Computation of several Hessenberg determinants
Artikel in diesem Heft
- Regular papers
- Fuzzy deductive systems of RM algebras
- Congruence pairs of principal MS-algebras and perfect extensions
- The lattices of 𝔏-fuzzy state filters in state residuated lattices
- Central lifting property for orthomodular lattices
- EQ-Modules
- On the exponential Diophantine equation Pxn + Pxn+1 + ⋯ + Pxn+k-1 = Pm
- Remarks on some generalization of the notion of microscopic sets
- Disjointness of composition operators on Hv0 spaces
- A common fixed point theorem for non-self mappings in strictly convex menger PM-spaces
- The Poincaré-Cartan forms of one-dimensional variational integrals
- Coarse cohomology with twisted coefficients
- Divisible extension of probability
- Asymptotic behavior of the records of multivariate random sequences in a norm sense
- Strong convergence of the functional nonparametric relative error regression estimator under right censoring
- A new kumaraswamy generalized family of distributions: Properties and applications
- Efficient message transmission via twisted Edwards curves
- Computation of several Hessenberg determinants
