Prime powers in sums of terms of binary recurrence sequences View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-03-16

AUTHORS

Eshita Mazumdar, S. S. Rout

ABSTRACT

Let (un)n≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(u_{n})_{n \ge 0}$$\end{document} be a non-degenerate binary recurrence sequence with positive discriminant and p be a fixed prime number. In this paper, we are interested in finding a finiteness result for the solutions of the Diophantine equation un1+un2+⋯+unt=pz\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u_{n_{1}} + u_{n_{2}} + \cdots + u_{n_{t}} = p^{z}$$\end{document} with n1>n2>⋯>nt≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n_1> n_2> \cdots > n_t\ge 0$$\end{document}. Moreover, we explicitly find all the powers of three which are sums of three balancing numbers using lower bounds for linear forms in logarithms. Further, we use a variant of the Baker–Davenport reduction method in Diophantine approximation due to Dujella and Pethő. More... »

PAGES

695-714

References to SciGraph publications

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URI

http://scigraph.springernature.com/pub.10.1007/s00605-019-01282-w

DOI

http://dx.doi.org/10.1007/s00605-019-01282-w

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112829619


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