Certain Diophantine equations involving balancing and Lucas-balancing numbers
نویسندگان
چکیده
منابع مشابه
On the Properties of Balancing and Lucas-Balancing $p$-Numbers
The main goal of this paper is to develop a new generalization of balancing and Lucas-balancing sequences namely balancing and Lucas-balancing $p$-numbers and derive several identities related to them. Some combinatorial forms of these numbers are also presented.
متن کاملOn Pell, Pell-Lucas, and balancing numbers
In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers. Moreover, we obtain the set of positive integer solutions of some specific Pell equations in terms of the integer sequences mentioned in the text.
متن کاملSome Congruences for Balancing and Lucas-balancing Numbers and Their Applications
Balancing numbers n and balancers r are solutions of the Diophantine equation 1 + 2 + . . . + (n 1) = (n + 1) + (n + 2) + . . . + (n + r). It is well-known that if n is a balancing number, then 8n2 + 1 is a perfect square and its positive square root is called a Lucas-balancing number. In this paper, some new identities involving balancing and Lucas-balancing numbers are obtained. Some divisibi...
متن کاملTridiagonal matrices related to subsequences of balancing and Lucas-balancing numbers
It is well known that balancing and Lucas-balancing numbers are expressed as determinants of suitable tridiagonal matrices. The aim of this paper is to express certain subsequences of balancing and Lucas-balancing numbers in terms of determinants of tridiagonal matrices. Using these tridiagonal matrices, a factorization of the balancing numbers is also derived.
متن کاملBalancing diophantine triples
In this paper, we show that there are no three distinct positive integers a, b and c such that ab + 1, ac + 1, bc + 1 all are balancing numbers.
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ژورنال
عنوان ژورنال: Acta et Commentationes Universitatis Tartuensis de Mathematica
سال: 2016
ISSN: 2228-4699,1406-2283
DOI: 10.12697/acutm.2016.20.14