On a variant of Pillai’s problem involving S-units and Fibonacci numbers
On a variant of Pillai’s problem involving S-units and Fibonacci numbers
Abstract Let us denote by $$F_n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> the n -th Fibonacci number. In this paper we show that there exist at most finitely many integers c such that the exponential Diophantine equation $$F_n-2^x3^y=c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>F</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>x</mml:mi> …