[/quote]
,
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 
concur. Compute 
.
interesting if 
is composite and for every divisor 
of 
and 
is also a divisor of 
to 
have the digit 
and are divisible by 
?
Y by akpi2, PikaPika999
Hi, I wanted to ask everyone, before the written competition, each state had to do their chant. What chant did you and your team make xd!
Im in WV and I think we did the least cringe chant, and it goes like this:
(After one person says something, the other person following waits ~2 seconds, and then says their line)
P1: Hi
P2: Hi
P3: Hi
P4: Bye
Lol if you were at the national competition you prob remember.
Im in WV and I think we did the least cringe chant, and it goes like this:
(After one person says something, the other person following waits ~2 seconds, and then says their line)
P1: Hi
P2: Hi
P3: Hi
P4: Bye
Lol if you were at the national competition you prob remember.
This post has been edited 1 time. Last edited by ilovebender, May 12, 2022, 1:09 AM
