Difference between revisions of "1997 AIME Problems/Problem 14"
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== Problem == | == Problem == | ||
| + | Let <math>\displaystyle v</math> and <math>\displaystyle w</math> be distinct, randomly chosen roots of the equation <math>\displaystyle z^{1997}-1=0</math>. Let <math>\displaystyle \frac{m}{n}</math> be the probability that <math>\displaystyle\sqrt{2+\sqrt{3}}\le\left|v+w\right|</math>, where <math>\displaystyle m</math> and <math>\displaystyle n</math> are relatively prime positive integers. Find <math>\displaystyle m+n</math>. | ||
== Solution == | == Solution == | ||
Revision as of 19:58, 7 March 2007
Problem
Let 
and 
be distinct, randomly chosen roots of the equation 
. Let 
be the probability that 
, where 
and 
are relatively prime positive integers. Find 
.
