Poldavia is a strange kingdom. Its currency unit is the bourbaki and there exist only two types of coins: gold ones and silver ones. Each gold coin is worth
bourbakis and each silver coin is worth
bourbakis (
and
are positive integers). Using gold and silver coins, it is possible to obtain sums such as 10000 bourbakis, 1875 bourbakis, 3072 bourbakis, and so on. But Poldavia’s monetary system is not as strange as it seems:
(a) Prove that it is possible to buy anything that costs an integral number of bourbakis, as long as one can receive change.
(b) Prove that any payment above
bourbakis can be made without the need to receive change.
