Certain Diophantine equations involving balancing and Lucas-balancing numbers | Zendy

Prasanta Kumar Ray | Zendy

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Certain Diophantine equations involving balancing and Lucas-balancing numbers

Author(s) -

Prasanta Kumar Ray

Publication year - 2016

Publication title -

acta et commentationes universitatis tartuensis de mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.276

H-Index - 6

eISSN - 2228-4699

pISSN - 1406-2283

DOI - 10.12697/acutm.2016.20.14

Subject(s) - diophantine equation , lucas sequence , mathematics , diophantine set , lucas number , square root , discrete mathematics , combinatorics , geometry , fibonacci number , fibonacci polynomials , orthogonal polynomials , difference polynomials

It is well known that if x is a balancing number, then the positive square root of 8x2 + 1 is a Lucas-balancing number. Thus, the totality of balancing number x and Lucas-balancing number y are seen to be the positive integral solutions of the Diophantine equation 8x2 +1 = y2. In this article, we consider some Diophantine equations involving balancing and Lucas-balancing numbers and study their solutions.

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