Cullen numbers and Woodall numbers in generalized Fibonacci sequences

Recently Bilu, Marques and Togbé [4] gave a general effective finiteness result on the equationFn(k)=Cm, where Fn(k) denotes the k-generalized Fibonacci-sequence and Cm the sequence of Cullen numbers, by giving explicit absolute bounds for n,k,m. However, the authors in [4] explained that their bounds were too large to use Dujella-Pethő reduction to completely solve the equation in question. In the present paper, using the bounds established by Bilu, Marques and Togbé in [4] and a different approach based on 2-adic analysis, we completely solve this equation. Further, using the same approach we also solve the corresponding equation for Woodall numbers.