On the \(X\)-coordinates of Pell equations of the form \(px^2\)

DOI10.1007/s10998-022-00473-7OpenAlexW4283311227MaRDI QIDQ2694923

Yongzhong Hu, Maohua Le

Publication date: 4 April 2023

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10998-022-00473-7

zbMATH Keywords

quartic Diophantine equation\(X\)-coordinates of Pell equation

Mathematics Subject Classification ID

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

Cites Work

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• $X$-coordinates of Pell equations as sums of two tribonacci numbers
• Linear combinations of prime powers in \(X\)-coordinates of Pell equations
• Zeckendorf representations with at most two terms to \(x\)-coordinates of Pell equations
• On Pillai's problem with \(X\)-coordinates of Pell equations and powers of 2
• On the \(x\)-coordinates of Pell equations which are \(k\)-generalized Fibonacci numbers
• The Diophantine equation x⁴ - Dy² = 1, II
• Applications of Jacobi's symbol to Lehmer's numbers
• The Diophantine equation $b^2X^4-dY^2=1$
• On the $x$-coordinates of Pell equations which are Fibonacci numbers
• The Fibonacci numbers and the Arctic Ocean
• On the $x$--coordinates of Pell equations which are products of two: Lucas numbers, Pell numbers
• On the $X$-coordinates of Pell equations which are Tribonacci numbers
• Lucas and fibonacci numbers and some diophantine Equations

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