Representability in coin systems with two denominations

Abstract

Given unlimited coins of perscribed type, some amounts may not be representable. We will deal with coin systems with only two denominations.

There are formulae for highest nonrepresentable amount and nonrepresentable amounts count in that case. We will show different approaches to show this: first we will use geometry.

In second part we will prove both formulae using divisibility. In the third part we use generating functions to do the same.

Keywords

• representability
• geometry
• generating functions
• Frobenius number
• divisibility