Question 109
Alexander and Denitza play the following game. Alexander cuts (if possible) a band of positive integer length to three bands of positive integer lengths such that the largest band is unique. Then Denitza cuts (if possible) the largest band in the same way and so on. The winner is the one who makes the last move. Consider the bands whose lengths are integers of the form $a^b$, $a-1, b-1 \in \mathbb{N}$. For which of them Denitza has a winning strategy.