JEE Novice - (12)

Algebra Level 4

Given that

\[ \sum_{i=1}^{2003} i^2 = (2003)(4007)(334), \]

find the value of \(x\) that satisfies

\[ (1)(2003) + (2)(2002)+ (3)(2001) \dots (2003)(1) = (2003)(334)(x). \]