Difference between revisions of "Mock AIME 6 2006-2007 Problems/Problem 7"
(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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==Solution== | ==Solution== | ||
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| + | The solution of <math>P_n(x)</math> will be in the form <math>x=e^{\frac{2\pi k}{n+1}}</math> for <math>k=1,2,\cdots,n</math> | ||
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| + | ~Tomas Diaz. orders@tomasdiaz.com | ||
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| + | {{alternate solutions}} | ||
Revision as of 19:07, 26 November 2023
Problem
Let 
and 
for all integers 
. How many more distinct complex roots does 
have than 
?
Solution
The solution of 
will be in the form 
for 
~Tomas Diaz. orders@tomasdiaz.com
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
