How to change coins, M&M's, or chicken nuggets: The linear Diophantine problem of Frobenius

Factoring in the Chicken McNugget Monoid

“…, y k of (possibly negative) integers such that We have already shown that F ( ) = 43 and F ( 4, 7, 10 ) = 13. A famous result of Sylvester from 1884 [32] states that if a and b are relatively prime, then F ( a, b ) = ab − a − b (a nice proof of this can be found in [7]). This is where the fun begins, as strictly speaking no closed formula exists for the Frobenius number of numerical monoids that require 3 or more generators.…”