On X-coordinates of Pell equations which are repdigits

Gómez, Carlos A.; Luca, Florian; Zottor, Faith Shadow

doi:10.1007/s40993-020-00220-2

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2021

2022

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Cited by 3 publications

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“…We mention a few such recent results; the interested reader may consult their references. In the papers [1,2,3,4,5,6,8,11,15,16,19] the authors provide various finiteness results concerning the values (or sums or products of values) of certain concrete recurrence sequences (such as Fibonacci, Tribonacci, generalized Fibonacci, Lucas, Padovan, Pell, repdigits) in the x coordinate of equation (1), for the cases t = ±1, ±4. Concerning the y-coordinate, we are aware only of two related results.…”

Section: Introductionmentioning

confidence: 99%

Terms of recurrence sequences in the solution sets of generalized Pell equations

Hajdu

Sebestyén

2022

Int. J. Number Theory

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Section: Introductionmentioning

confidence: 99%

Terms of recurrence sequences in the solution sets of generalized Pell equations

Hajdu

Sebestyén

2022

Int. J. Number Theory

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X-coordinates of Pell Equations in Various Sequences

Luca

2021

Transcendence in Algebra, Combinatorics, Geometry and Number Theory

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Best Approximations by $\mathcal{F}_{p^l}$-Continued Fractions

Kushwaha¹,

Sarma²

2021

Preprint

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In this article, for a certain subset X of the extended set of rational numbers, we introduce the notion of best X -approximations of a real number. The notion of best X -approximation is analogous to that of best rational approximation. We explore these approximations with the help of F p l -continued fractions, where p is a prime and l ∈ N, we show that the convergents of the F p l -continued fraction expansion of a real number x satisfying certain maximal conditions are exactly the best F p l -approximations of x.

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On X-coordinates of Pell equations which are repdigits

Cited by 3 publications

References 8 publications

Terms of recurrence sequences in the solution sets of generalized Pell equations

Terms of recurrence sequences in the solution sets of generalized Pell equations

X-coordinates of Pell Equations in Various Sequences

Best Approximations by $\mathcal{F}_{p^l}$-Continued Fractions

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