Diophantine equations with binary recurrences associated to the Brocard–Ramanujan problem

  • László Szalay

    University of West Hungary, Sopron, Hungary

Abstract

In this paper, applying the Primitive Divisor Theorem, we solve completely the diophantine equation

in non-negative integers , and if the binary recurrence is either the Fibonacci sequence, or the Lucas sequence, or it satisfies the recurrence relation with , and an arbitrary positive integer . The more specific case

was investigated by Marques [3] in Portugaliae Mathematica in the case of the Fibonacci sequence.

Cite this article

László Szalay, Diophantine equations with binary recurrences associated to the Brocard–Ramanujan problem. Port. Math. 69 (2012), no. 3, pp. 213–220

DOI 10.4171/PM/1914