Solving Frobenius Equations and Computing Frobenius Numbers
A Frobenius equation is an equation of the form
where 
, ..., 
are positive integers, 
is an integer, and the coordinates 
, ..., 
of solutions are required to be non-negative integers.
The Frobenius number of 
, ..., 
is the largest integer 
for which the Frobenius equation 
has no solutions.
| FrobeniusSolve[{a1,...,an},b] | give a list of all solutions of the Frobenius equation  |
| FrobeniusSolve[{a1,...,an},b,m] | give  solutions of the Frobenius equation  ; if less than  solutions exist, give all solutions |
| FrobeniusNumber[{a1,...,an}] | give the Frobenius number of  , ...,  |
Functions for solving Frobenius equations and computing Frobenius numbers.
This gives all solutions of the Frobenius equation
.
| Out[1]= |  |
This gives one solution of the Frobenius equation
.
| Out[2]= |  |
Here is the Frobenius number of
, that is, the largest
for which the Frobenius equation
has no solutions.
| Out[3]= |  |
This shows that indeed, the Frobenius equation
has no solutions.
| Out[4]= |  |
Here are all the ways of making 42 cents change using 1, 5, 10, and 25 cent coins.
| Out[5]= |  |
Using 24, 29, 31, 34, 37, and 39 cent stamps, you can pay arbitrary postage of more than 88 cents.
| Out[6]= |  |
