MathDB
Theta Function

Source:

April 8, 2008
functionmodular arithmetic

Problem Statement

For a positive integer n n, let θ(n) \theta(n) denote the number of integers 0≤x<2010 0 \leq x < 2010 such that x^2 \minus{} n is divisible by 2010 2010. Determine the remainder when \displaystyle \sum_{n \equal{} 0}^{2009} n \cdot \theta(n) is divided by 2010 2010.
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