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

0

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100

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503

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1006

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Solution

The correct option is C $503$

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