# A problem by Fatin Farhan

Level pending

Let $$5,8,11, . .$$ and $$9,17,25,. . .$$ be two arithmetic progressions. The set $$S$$ is the union of the first $$2004$$ terms of each sequence and $$N$$ be the number of distinct numbers are in $$S$$. What is the last three digits of $$N$$?

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