Frobenius Number

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)

REFERENCES:

Sylvester, J. J. "Question 7382." Mathematical Questions from the Educational Times 41, 21, 1884.