PERFECT POWERS in PRODUCTS of TERMS of ELLIPTIC DIVISIBILITY SEQUENCES

Authors

Lajos Hajdu, Debreceni Egyetem Természettudományi és Technológiai Kar
Shanta Laishram, Indian Statistical Institute (Delhi Centre)
Márton Szikszai, Debreceni Egyetem Természettudományi és Technológiai Kar

Article Type

Research Article

Publication Title

Bulletin of the Australian Mathematical Society

Abstract

Diophantine problems involving recurrence sequences have a long history. We consider the equation in positive integers with and, where is a fixed integer and is an elliptic divisibility sequence, an important class of nonlinear recurrences. We prove that the equation admits only finitely many solutions. In fact, we present an algorithm to find all possible solutions, provided that the set of th powers in is given. We illustrate our method by an example.

First Page

395

Last Page

404

DOI

10.1017/S0004972716000332

Publication Date

12-1-2016

Comments

Open Access; Green Open Access

Recommended Citation

Hajdu, Lajos; Laishram, Shanta; and Szikszai, Márton, "PERFECT POWERS in PRODUCTS of TERMS of ELLIPTIC DIVISIBILITY SEQUENCES" (2016). Journal Articles. 4378.
https://digitalcommons.isical.ac.in/journal-articles/4378