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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