Internationale Mathematik-Olympiade

Let $(a, b, c)$ be pairwise relatively prime positive integers. Let $(kabc - ab - bc - ca)$ be the largest integer that cannot be expressed in the form $(xbc + yca + zab)$ where $(x, y, z)$ are nonnegative integers, where $k$ is a fixed natural number.

Evaluate $2k^{9}$ .

Calculator can be used. Brackets( ) are used just to make the expressions look nice. It has no mathematical relations.