Difference between revisions of "AoPS Wiki talk:Problem of the Day/September 11, 2011"
(Created page with "We put the number in Polar form: <math>r(cis{\theta})</math>. Then <math>(a+bi)^{2002}=r^{2002}(cis(2002\theta))=r(cis(-\theta))</math>. Since <math>r^{2002}=r</math>, eith...") |
(No difference)
|
Revision as of 13:03, 11 September 2011
We put the number in Polar form: . Then
. Since
, either
or
. If
, then we have
. We can now just focus on
, since
gives the same solutions.
Since ,
for some
. Each value of
between 1 and 2003 gives a unique solution, so
has
solutions for
. Thus, there are
solutions;
.