JournalspmVol. 69 / No. 3DOI 10.4171/pm/1914

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

  • László Szalay

    University of West Hungary, Sopron, Hungary
Diophantine equations with binary recurrences associated to the Brocard–Ramanujan problem cover

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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.