Work

Sum of terms of recurrence sequences in the solution sets of generalized Pell equations

Year: 2025

Type: article

Abstract: Let (Xk)k⩾1 and (Yk)k⩾1 be sequences of X and Y-coordinates of the positive integer solutions (x,y) of the equation x2−dy2=t. In this paper, we completely describe these recurrence sequences such that the sums of two terms of recurrence sequences in the solution sets of generalized Pell equations are infinitely many. Further, we give an upper bound for the number of such terms when there are only finitely many of them. This work is motivated by the recent paper of Hajdu and Sebestyén (Int. J. Number Theory 18 (2022), 1605-1612).

Source: Functiones et Approximatio Commentarii Mathematici

DOI: 10.7169/facm/241002-24-3

Authors: Pritam Kumar Bhoi, Rudranarayan Padhy, Sudhansu Sekhar Rout

Institutions: National Institute of Technology Rourkela, National Institute of Technology Calicut

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Board for Higher Mathematics, National Institute of Technology Calicut, Science and Engineering Research Board

OpenAlex ID: W4411334144

FWCI:

Cites: 19

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Related to: 10