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Mock AIME 6 2006-2007 Problems/Problem 7

Revision as of 09:23, 23 November 2023 by Tomasdiaz (talk | contribs) (Created page with "==Problem == Let <math>P_n(x)=1+x+x^2+\cdots+x^n</math> and <math>Q_n(x)=P_1\cdot P_2\cdots P_n</math> for all integers <math>n\ge 1</math>. How many more distinct complex ro...")
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Problem

Let $P_n(x)=1+x+x^2+\cdots+x^n$ and $Q_n(x)=P_1\cdot P_2\cdots P_n$ for all integers $n\ge 1$. How many more distinct complex roots does $Q_{1004}$ have than $Q_{1003}$?

Solution

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