Question 11
Given two positive integers $a$ and $b$, a legal move is to choose a proper divisor of one of them and add it to either $a$ or $b$. Players $A$ and $B$ make legal moves in turns; $A$ plays first. The one who obtains a number $\ge 2015$ wins. Determine who wins if the game starts with:
$$
a) a=3, b=5; \qquad b) a=6, b=7.
$$
(Here a proper divisor of $k \in \mathbb{N}$ means a $d \in \mathbb{N}$ such that $d$ divides $k$ and $d \neq k$.)
$$
a) a=3, b=5; \qquad b) a=6, b=7.
$$
(Here a proper divisor of $k \in \mathbb{N}$ means a $d \in \mathbb{N}$ such that $d$ divides $k$ and $d \neq k$.)