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arXiv · 2403.18924

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

Pritam Kumar Bhoi·Rudranarayan Padhy·Sudhansu Sekhar Rout
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Abstract

Let $(X_{k})_{k\geq 1}$ and $(Y_k)_{k\geq 1}$ be the sequence of $X$ and $Y$-coordinates of the positive integer solutions $(x, y)$ of the equation $x^2 - dy^2 = t$. In this paper we completely describe those recurrence sequences such that sums of two terms 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 Hajdu and Sebestyén (Int. J. Number Theory 18 (2022), 1605-1612).

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Pritam Kumar Bhoi, Rudranarayan Padhy, Sudhansu Sekhar Rout. 2024-09-18. Sum of terms of recurrence sequences in the solution sets of generalized Pell equations. https://arxiv.org/abs/2403.18924

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