be a triangle with incenter 
,
and circumcircle 
.
be the midpoints of sides 
,
,
and let 
be the tangency points of 
be the intersections of line 
with line 
and line 
,
be the midpoint of arc 
of 
.
bisects 
.
be the set of integers, and let 
be a function. Prove that there are infinitely many integers 
such that the function 
defined by 
is not bijective.
,
such that 
.
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Congratulations to all of you!!!!!!!
Alexander Wang
Hannah Fox
Karn Chutinan
Andrew Lin
Calvin Wang
Tiger Zhang
Good luck in Australia!
Alexander Wang
Hannah Fox
Karn Chutinan
Andrew Lin
Calvin Wang
Tiger Zhang
Good luck in Australia!
Have fun!
