In the expansion of $(ax + b)^{2000},$ where $a$ and $b$ are [relatively prime](https://artofproblemsolving.com/wiki/index.php/Relatively_prime) positive integers, the [coefficients](https://artofproblemsolving.com/wiki/index.php/Coefficient) of $x^{2}$ and $x^{3}$ are equal. Find $a + b$.
Using the [binomial theorem](https://artofproblemsolving.com/wiki/index.php/Binomial_theorem), $\binom{2000}{1998} b^{1998}a^2 = \binom{2000}{1997}b^{1997}a^3 \Longrightarrow b=666a$.
Since $a$ and $b$ are positive relatively prime integers, $a=1$ and $b=666$, and $a+b=\boxed{667}$.