Linear Diophantine Problems

The Frobenius number g(A k ) Let A k \({A_k} = \{ {a_1},...,{a_k}\}\subset\) IN with gcd(A k ) = 1, n\( \in I{N_0}.\) If $$n = \sum\limits_{i = 1}^k {{x_i}{a_i},{x_i}}\in I{N_0}$$ (1) we call this a representation or a g-representation of n by Ak (in order to distinguish between several types of representations that will be considered in the sequel). Then the Frobenius number g(A k ) is the greatest integer with no g-representation.