Frobenius numbers are solutions to the coin problem. Let be coin denominations; what is the smallest sum of money that cannot be obtained using these coins? More formally, define the Frobenius number as the greatest number that is not a linear combination with . The Frobenius number exists if and only if and . A special case of Frobenius numbers involves the interestingly named McNugget numbers, and there is a well-known formula when given by sometimes known as the Chicken McNugget Theorem.
Everyone knows what continued fractions are, right? Continued fractions have interesting properties and can be used to obtain best rational approximations for real numbers, among other things. Here is an example of a finite continued fraction: