Start Counting! Part-3

Algebra Level 4

Find the number of Quadratic polynomials,\(ax^2+bx+c\) which satisfy the following conditions:

  1. \(a,b,c\) are distinct.

  2. \(a,b,c\) belongs to \( \{1,2,3,\ldots,1999 \} \).

  3. \(x+1\) divides \(ax^2+bx+c\).

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