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Partial sums of a recurrent sequence

Source:

March 14, 2006
modular arithmetic

Problem Statement

A sequence of integers a1a_1, a2a_2, a3a_3, …\ldots is chosen so that an=an−1−an−2a_n = a_{n - 1} - a_{n - 2} for each n≥3n \ge 3. What is the sum of the first 2001 terms of this sequence if the sum of the first 1492 terms is 1985, and the sum of the first 1985 terms is 1492?
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