Abstract
On a Diophantine equation related to the difference of two Pell numbers
Highlights
Many researchers investigated the solutions of Diophantine equations of the form un ± um = pa where is a fixed linear recurrence sequence and p is a prime
The main argument used for the solution of such problems is Baker’s theory and a version of the Baker-Davenport reduction method
We obtain all solutions of the Diophantine equation Pn − Pm = 3a
Summary
Many researchers investigated the solutions of Diophantine equations of the form un ± um = pa where (un) is a fixed linear recurrence sequence and p is a prime. Bravo and Luca [3, 4] solved the equation un + um = 2a for the cases when (un) is the Fibonacci sequence and when (un) is the Lucas sequence. Bitim and Keskin [1] found all the solutions of the equation un − um = 3a for the case when (un) is the Fibonacci sequence. Many other researches on this topic, such as [6], have been carried out. The main argument used for the solution of such problems is Baker’s theory (lower bound for the absolute value of linear combinations of logarithms of algebraic numbers) and a version of the Baker-Davenport reduction method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
