Q: Show that if a, b, c \in Z^+ and (a, b) = 1, then the number of n nonnegative solutions of ax + by = c satisfies the inequality: \frac{c}{ab} - 1 < n \leq \frac{c}{ab} + 1

Some Useful facts:
Intercepts @ (c/a, 0) and (o, c/b)

Distance between intercepts is: \frac{c}{ab}*\sqrt{a^2 + b^2}

Distance between successive points: \frac{1}{d}*\sqrt{a^2 + b^2}

There is an integral point x,y on the line and in the first quadrant if:
\frac{c}{ab}*\sqrt{a^2 + b^2} > \frac{1}{d}*\sqrt{a^2 + b^2}<br />