Linear Diophantine Equations

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

Some Useful facts:

Intercepts @ (c/a, 0) and (o, c/b)

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

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

There is an integral point x,y on the line and in the first quadrant if:

$\displaystyle \frac{c}{ab}*\sqrt{a^2 + b^2}$ $\displaystyle > \frac{1}{d}*\sqrt{a^2 + b^2}

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