You should use FrobeniusNumber
instead of FrobeniusSolve
, since it serves this purpose
The Frobenius number of $a_{1}, ... a_{n}$,.is the largest integer b for which the Frobenius equation $a_{1} x_{1}+ ... a_{n} x_{n} = k$ has no non-negative integer solutions. The $a_{i}$ must be positive integers.
FrobeniusNumber[{6, 9, 20}]
43
Nevertheless you can still get the result playing with FrobeniusSolve
, there might be many possible ways, let's point out one of them using Cases
with an appropriate replacement rule e.g.
Max @ Cases[ Table[{ k, FrobeniusSolve[{6, 9, 20}, k] != {}}, {k, 100}], {a_, False} -> a]
43
In case of not knowing FrobeniusNumber
, one can get an idea also with Reduce
or Solve
although these ways are not recommended for diophantine equations, see e.g. Finding the number of solutions to a diophantine equation.
FrobeniusNumber[{6, 9, 20}]
. $\endgroup$