Additive Diophantine Equations involving S-Units, Factorials and Ternary Recurrences with repeated root

Vikas Godara, Divyum Sharma

Let $C_n=n{2}^n+1$ denote the $n$th Cullen number. There has been recent interest in finding all Cullen numbers having a given Diophantine property. We prove that, for a fixed intege…