AoPS Academy
sigmas = 
looksmaxxers, and 
looksmaxxers = 
skibdis, how many skibidis are in a sigma? Express your answer as a common fraction
+1 w
consists of the union of disjoint pieces. Compute the distance between the endpoints of any one piece
and 
are in the coordinate plane such that 
. Let 
denote the locus of all points 
in the coordinate plane satisfying 
, and let 
be the midpoint of 
. Points 
and 
are on such that 
and 
. The value of 
can be expressed in the form 
, where 
and 
are relatively prime positive integers. Find 
.
. The smallest natural numebr such that they leave distinct remainders when divided by is:
Where 
are positive integers and 
is a non-square positive integer. If 
denotes the n-th set of solution to the equation with 
Then, prove that 
and 
Show that
Let 
Show that
Prove that
. Prove that
You even figured out how to use emoticons in your profile. (which took me like, half a month to figure out 
