A certain Sultan wished to send into battle an army that could be formed
into two perfect squares in twelve different ways. What is the smallest
number of men of which that army could be composed? To make it clear to
the novice, I will explain that if there were 130 men, they could be
formed into two squares in only two different ways--81 and 49, or 121
and 9. Of course, all the men must be used on every occasion.