Question 109
Anna and Elie play a game. They are both given the same set $A$ consisting of finitely many distinct positive integers. Anna secretly chooses an integer $a \in A$. If Elie chooses an integer $b$ (not necessarily in $A$) and gives it to Anna, Anna gives him the number of positive divisors of $ab$. Show that Elie can choose $b$ so as to recover with certainty the integer chosen by Anna.