\(X\)-coordinates of Pell equations in various sequences

DOI10.1007/978-3-030-84304-5_19OpenAlexW3208234824MaRDI QIDQ2097087

Florian Luca

Publication date: 11 November 2022

Full work available at URL: https://doi.org/10.1007/978-3-030-84304-5_19

zbMATH Keywords

linear recurrencesrepdigitsFibonacci numbers and variationsPell equations in various sequences

Mathematics Subject Classification ID

Recurrences (11B37) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Cites Work

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• Elliptic curves over finite fields with Fibonacci numbers of points
• Intersection des images de certaines suites recurrentes linéaires
• Perfect squares representing the number of rational points on elliptic curves over finite field extensions
• On members of Lucas sequences which are products of factorials
• On \(X\)-coordinates of Pell equations which are repdigits
• On \(Y\)-coordinates of Pell equations which are members of a fixed binary recurrence
• Zeckendorf representations with at most two terms to \(x\)-coordinates of Pell equations
• On the \(x\)-coordinates of Pell equations which are products of two Fibonacci numbers
• On the \(x\)-coordinates of Pell equations which are \(k\)-generalized Fibonacci numbers
• On the solutions of the congruence 𝑛²≡1(𝑚𝑜𝑑𝜙²(𝑛))
• Logarithmic forms and group varieties.
• On Y-coordinates of Pell equations which are base 2 rep-digits
• On $X$-coordinates of Pell equations which are repdigits
• On the $x$-coordinates of Pell equations which are rep-digits
• On the $x$-coordinates of Pell equations which are Fibonacci numbers
• Intersections of recurrence sequences
• On the $X$-coordinates of Pell equations which are Tribonacci numbers
• Number Theory
• Pell's equation

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