such that there exist infinitely many rational numbers 
satisfying![\[
\left| \frac{q}{p} - \frac{\sqrt{5} - 1}{2} \right| < \frac{\alpha}{p^2}.
\]](http://latex.artofproblemsolving.com/1/1/6/1162c6a7215bff2f9fdaa042a6952f86524e9e92.png)
such that
are all powers of 
.
be a convex quadrilateral. Let 
be the midpoints of 
respectively. If 
concur at a point 
prove that 
,
children standing in a circle. For each girl, it turns out that among the five people following her clockwise, there are more boys than girls. Find the greatest number of girls that can stand in a circle.
so that there exists a unique 
satisfying 
and![\[f(x+g(y))+f(-x-g(-y))=g(x+f(y))+g(-x-f(-y))\]](http://latex.artofproblemsolving.com/d/e/0/de0ea33c3a679ff02762be39e9013b72974e4287.png)
for all 
.
be a triangle with circumcircle 
and incenter 
and let 
be the midpoint of 
.
,
,
are selected on sides 
,
such that 
,
,
.
intersects 
other than 
.
and 
meet on 
interesting if 
is composite and for every divisor 
of 
and 
is also a divisor of 
Y by Generic_Username, DrMath, mathwiz_aku, whiteawesomesun, trumpeter, Mudkipswims42, AstroCarp, hodori01, ilike3.1415926, Adventure10, Mango247
The MAA AMC program very much appreciates the increasing interest in international participation in our competitions.
Unfortunately, the rapid growth in interest and participation has made it unfeasible for our internal resources to manage the program as it currently operates. We are reevaluating the international registration and competition administration model during the 2016-2017 cycle.
For the 2016-2017 competition cycle, the MAA AMC exams will only be offered to schools with a USA, Canada, APO/FPO/DPO mailing addresses and schools registered with one of the five AMC international partners. If your school is in one of the areas represented by an AMC international partner, please contact the group manager directly for information on participating in the AMC program this year.
Thank you for your patience as we assess our options to successfully offer the AMC exams to more international audiences in the future. For more information: http://www.maa.org/math-competitions/international-registrations
Unfortunately, the rapid growth in interest and participation has made it unfeasible for our internal resources to manage the program as it currently operates. We are reevaluating the international registration and competition administration model during the 2016-2017 cycle.
For the 2016-2017 competition cycle, the MAA AMC exams will only be offered to schools with a USA, Canada, APO/FPO/DPO mailing addresses and schools registered with one of the five AMC international partners. If your school is in one of the areas represented by an AMC international partner, please contact the group manager directly for information on participating in the AMC program this year.
Thank you for your patience as we assess our options to successfully offer the AMC exams to more international audiences in the future. For more information: http://www.maa.org/math-competitions/international-registrations
