 TOPICS  # 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)

Coin Problem, Frobenius Equation, Greedy Algorithm, McNugget Number, Postage Stamp Problem

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## References

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

Frobenius Number

## Cite this as:

Weisstein, Eric W. "Frobenius Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FrobeniusNumber.html