Find the largest positive integer $N$ such that the equation $99x + 100y + 101z = N$ has an unique solution in the positive integers $x, y, z$. (7 points)
Source: Fall 2005 Tournament of Towns Junior A-Level #5
Tags: number theory
Find the largest positive integer $N$ such that the equation $99x + 100y + 101z = N$ has an unique solution in the positive integers $x, y, z$. (7 points)