# A seemingly simple question

Number Theory Level 3

Positive integers $$a, b, c,$$ and $$d$$ satisfy $$a > b > c > d$$, $$a + b + c + d = 2010$$, and $$a^2 - b^2 + c^2 - d^2 = 2010$$. Find the number of possible values of $$a$$.

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