Frobenius Number
المؤلف:
Sylvester, J. J.
المصدر:
"Question 7382." Mathematical Questions from the Educational Times 41, 21, 1884.
الجزء والصفحة:
...
28-5-2020
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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[![<span style=]()
{" src="https://mathworld.wolfram.com/images/equations/FrobeniusNumber/Inline7.gif" style="height:15px; width:5px" />a1, ..., an![<span style=]()
}" src="https://mathworld.wolfram.com/images/equations/FrobeniusNumber/Inline8.gif" style="height:15px; width:5px" />].
Sylvester (1884) showed
REFERENCES:
Sylvester, J. J. "Question 7382." Mathematical Questions from the Educational Times 41, 21, 1884.
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