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 :
This gives one solution of the Frobenius equation :
Here is the Frobenius number of , that is, the largest for which the Frobenius equation has no solutions:
This shows that indeed, the Frobenius equation has no solutions:
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