The number of natural number $n$ in the interval $[1005, 2010]$ for which the polynomial. $1+x+x^2+x^3+\ldots+x^{n-1}$ divides the polynomial $1+x^2+x^4+x^6+\ldots+x^{2010}$ is

  • [KVPY 2010]
  • A

    $0$

  • B

    $100$

  • C

    $503$

  • D

    $1006$

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