Suppose a country only issued two types of coins to be used as currency: one 7 unit coin and one 11 unit coin. This would cause a dilemma since certain prices could
not be paid exactly, such as 13 units. What would be the highest price that could not be paid with any combination of the two coins? Could you find any rule to follow? *
Let a and b be integers satisfying a>1 and b>1. Such a "highest prize" exists if and only if a and b are relatively prime. In this case, it is ab-a-b. For example, when a=11 and b=7, we get ab-a-b=59; when a=5 and b=9, we get ab-a-b=31.