The X -coordinates of Pell equations and Padovan numbers

DOI10.3906/mat-1808-2zbMath1448.11069OpenAlexW2909609613WikidataQ128536595 ScholiaQ128536595MaRDI QIDQ5742926

Salah Eddine Rihane, Alain S. Togbé, Mohand-Ouamar Hernane

Publication date: 8 May 2019

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-1808-2

zbMATH Keywords

Pell equationreduction methodlinear form in logarithmsPadovan numbers

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Arithmetic functions; related numbers; inversion formulas (11A25) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Linear forms in logarithms; Baker's method (11J86)

Related Items (4)

On the X-coordinates of Pell equations X2 − dY2 = ±1 as difference of two Fibonacci numbers ⋮ The \(x\)-coordinates of Pell equations and sums of two Fibonacci numbers. II. ⋮ Unnamed Item ⋮ On the \(x\)-coordinates of Pell equations that are sums of two Padovan numbers

Cites Work

• Unnamed Item
• Classical and modular approaches to exponential Diophantine equations. I: Fibonacci and Lucas perfect powers
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• Linear forms in two logarithms and interpolation determinants II
• 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
• On the $X$-coordinates of Pell equations which are Tribonacci numbers
• On the $x$-coordinates of Pell equations which are Fibonacci numbers II

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