The Frobenius number is the largest value 
for which the Frobenius equation
 | (1) |
has no solution, where the 
are positive integers, 
is an integer, and the solutions 
are nonnegative integer. As an example, if the 
values are 4 and 9, then 23 is the largest unsolvable number. Similarly, the largest number that is not a McNugget number (a number obtainable by adding multiples of 6, 9, and 20) is 43.
Finding the Frobenius number of a given problem is known as the coin problem.
Computation of the Frobenius number 
is implemented in the Wolfram Language as FrobeniusNumber[
a1, ..., an
].
Sylvester (1884) showed
 |  |  | (2) |
 |  |  | (3) |
