TR-MO-R1 2010 Problem 23

$1 \le n \le 2010$ koşulunu sağlayan kaç tane $n$ tam sayısı için $1^2-2^2+3^2-4^2+\cdots+(2n-1)^2-(2n)^2$ sayısı $2010$ ile bölünür?

a) $9$ b) $8$ c) $7$ d) $6$ e) $5$

Official text Turkish Mathematical Olympiad, first round 2010 official paper, page 7. Quoted with source.

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