# Random Number Generation

The "random" numbers produced by computers aren't purely random. They are actually pseudo-random, meaning that they are produced by mathematical formulas that simulate randomness.

The linear congruential generator takes a seed $$X_0$$ and generates subsequent pseudo-random numbers using the formula: $X_{n + 1} = (aX_n + c) \mod m$

$$X_1$$ is the first pseudo-random number generated, $$X_2$$ is the second, and so on.

Let R be the 2000th pseudo-random number generated by the linear congruential generator when $$X_0 = 42$$, $$a = 25$$, $$c = 31$$, and $$m = 2^{20}$$. What are the last three digits of R?

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