# Difference between revisions of "2005 AIME II Problems/Problem 9"

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== Problem == | == Problem == | ||

− | + | For how many positive integers <math> n </math> less than or equal to 1000 is <math> (\sin t + i \cos t)^n = \sin nt + i \cos nt </math> true for all real <math> t </math>? | |

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== Solution == | == Solution == | ||

== See Also == | == See Also == | ||

*[[2005 AIME II Problems]] | *[[2005 AIME II Problems]] |

## Revision as of 22:26, 8 July 2006

## Problem

For how many positive integers less than or equal to 1000 is true for all real ?