The Frobenius number is the largest value 
for which the Frobenius
equation
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(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
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(2)
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(3)
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