Multiplicative relations on binary recurrences

• Autorzy: Florian Luca , Volker Ziegler
• Języki publikacji: EN

Abstrakty

EN

Given a binary recurrence ${u_n}_{n≥0}$, we consider the Diophantine equation
$u_{n_1}^{x_1} ⋯ u_{n_L}^{x_L} = 1$
with nonnegative integer unknowns $n_1,..., n_L$, where $n_i ≠ n_j$ for 1 ≤ i < j ≤ L, $max{|x_i|: 1 ≤ i ≤ L} ≤ K$, and K is a fixed parameter. We show that the above equation has only finitely many solutions and the largest one can be explicitly bounded. We demonstrate the strength of our method by completely solving a particular Diophantine equation of the above form.

Kategorie tematyczne

• 11B37: Recurrences
• 11J25: Diophantine inequalities
• 11D57: Multiplicative and norm form equations
• 11D75: Diophantine inequalities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 2
• Strony: 183-199

Daty

wydano

2013

Twórcy

autor

Florian Luca

• Mathematical Institute, UNAM, Mexico, DF, 04510, Mexico

autor

Volker Ziegler

• Johann Radon Institute for, Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstr. 69, A-4040 Linz, Austria

Identyfikatory

DOI

10.4064/aa161-2-4