The Frobenius problem
Definition
Given a positive integers set {a_{1}, a_{2}, ... a_{p}}, the
Frobenius problem asks what is the largest integer N for which the equation
a_{1}.x_{1} + a_{2}.x_{2} + .. + a_{p}.x_{p} = N
has no positive integers {x_{1}, x_{2}, ... x_{p}} solution.
If the p numbers {a_{1}, a_{2}, ..., a_{p}} are prime in their set,
then this largest integer called the Frobenius number is well defined and is denoted
g(a_{1}, a_{2}, ... a_{p}).This problem is also known as the coin
problem since the Frobenius number of a set {a_{1}, a_{2}, ... a_{p}}
can be seen as the largest money amount that cannot be obtained using only coins of given
denominations {a_{1}, a_{2}, ... a_{p}}.
If a_{1}= 6, a_{2}= 9 and a_{3}= 20, the list of number N for which the equation
6x_{1}+9x_{2}+20x_{3} = N has no positive integer solution is called the non
McNugget numbers.
The list is {1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37, 43} and is
refered as sequence A065003 in OEIS.
Mc Donald sells chicken McNugget in boxes of 6, 9 and 20, so the non McNugget numbers
are the numbers of McNuggets you cannot get buying any number of boxes.
Calculator
There are 2 options with the following calculator:

When the first radio button is checked, the calculator provides the Frobenius number
g(a_{1}, a_{2}, ... a_{p}) of the set {a_{1}, a_{2}, ...
a_{p}}, the list of all integers N for which the equation
a_{1}.x_{1} + a_{2}.x_{2} + .. + a_{p}.x_{p} = N
has no positive integer solution and the number NRI(a_{1}, a_{2}, ... a_{p})
of such nonrepresentable integers.

When the second radio button is checked, the calculator solves the equation
a_{1}.x_{1} + a_{2}.x_{2} + .. + a_{p}.x_{p} = N
for a given N.
References
The Frobenius problem
on Wikipedia
Schur's theorem:
Used to prove that g(a_{1}, a_{2}, ... a_{p}) is defined if and only if
GCD(a_{1}, a_{2}, ... a_{p}) = 1
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