L. Szalay

activity

20142026

most citedDiophantine triples with values in

k

-generalized Fibonacci sequences

8 citations · 25 across the 15 of their papers we have counts for

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Showing 2020Show all

2 papers · 1 filter

math.NT2020

Markoff-Rosenberger triples and generalized Lucas sequences

Hayder Hashim, László Szalay, Szabolcs Tengely

We consider the Markoff-Rosenberger equation $a x^{2} + b y^{2} + c z^{2} = d x y z$ with $(x, y, z) = (U_{i}, U_{j}, U_{k}),$ where $U_{i}$ denotes the $i$ -th generalized Lucas number of first/second kind. We…

math.NT2020

Resolution of the equation $(3^{x_{1}} - 1) (3^{x_{2}} - 1) = (5^{y_{1}} - 1) (5^{y_{2}} - 1)$

Kálmán Liptai, László Németh, Gökhan Soydan +1

Consider the diophantine equation $(3^{x_{1}} - 1) (3^{x_{2}} - 1) = (5^{y_{1}} - 1) (5^{y_{2}} - 1)$ in positive integers $x_{1} \leq x_{2}$ , and $y_{1} \leq y_{2}$ . Each side of the equation is a product of two…

Markoff-Rosenberger triples and generalized Lucas sequences

Resolution of the equation (3x1​−1)(3x2​−1)=(5y1​−1)(5y2​−1)

Resolution of the equation $(3^{x_{1}} - 1) (3^{x_{2}} - 1) = (5^{y_{1}} - 1) (5^{y_{2}} - 1)$