Difference between revisions of "1997 AIME Problems/Problem 14"
Ninja glace (talk | contribs) (→Solution) |
Ninja glace (talk | contribs) (→Solution) |
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z^{1997}&=&e^{2\pi ik}\ | z^{1997}&=&e^{2\pi ik}\ | ||
z&=&e^{\frac{2\pi ik}{1997}} | z&=&e^{\frac{2\pi ik}{1997}} | ||
− | \end{eqnarray*}<math> | + | \end{eqnarray*}<\math> |
== See also == | == See also == | ||
* [[1997 AIME Problems]]</math> | * [[1997 AIME Problems]]</math> |
Revision as of 19:10, 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 .
Solution
The solution requires the use of Euler's formula:
If , where k is any constant, the equation reduces to:
$
== See also ==
- [[1997 AIME Problems]]$ (Error compiling LaTeX. Unknown error_msg)