GCND

The *greatest common non-divisor* of two positive integers $X$ and $Y$ satisfying $X \ge 5$ and $Y \ge 5$, denoted $\text{gcnd}(X, Y)$, is defined to be the largest positive integer $Z$ satisfying the following conditions: - $Z \le X$ **or** $Z \le Y$, and - $X$ is not a multiple of $Z$ **and** $Y$ is not a multiple of $Z$. It can be proved that as long as $X$ and $Y$ are both $\ge 5$, $\text{gcn