[/quote]
,
such that
x>y>0
2
such that 
.
for all 
.
satisfies 
.
,
at 
,
be the midpoint of 
.
intersect 
at 
,
meet 
,
meet 
at 
.
are concurrent.
and 
divides
where 
denotes the number of positive integers that divide 
and 
.
be its circumcenter and 
its incenter.
be the radical center of its three mixtilinears and let 
be the isogonal conjugate of 
be the Gergonne point of the triangle 
is parallel with line 
.
is a square of an integer.
for which the following statement holds: there exists at least one triple 
of integers such that
and all triples 
are integers.
be a rational function with complex coefficients whose denominator does not have multiple roots. Let 
be the complex roots of 
and 
be the roots of 
.
is a simple root of ![\[ \sum_{k=1}^m \frac{1}{w_k - u_0} = 2\sum_{k = 1}^n\frac{1}{u_k - u_0}.\]](http://latex.artofproblemsolving.com/6/f/3/6f36b138d97a24d1941d21f7ffbc11530ca2adde.png)
be a tetrahedron with circumcenter 
and 
are interior points of the edges 
and 
,
and 
,
and 
,
then 
where 
Y by WiseTigerJ1
An unfair coin has a 
probability of coming up heads and 
probability of coming up tails. The expected number of flips necessary to first see the sequence 
in that consecutive order can be written as 
for relatively prime positive integers 
, 
. Find the number of factors of .
probability of coming up heads and 
probability of coming up tails. The expected number of flips necessary to first see the sequence 
in that consecutive order can be written as 
for relatively prime positive integers 
, 
. Find the number of factors of .
![$11x4 = 44 [b]C[/b]$](http://latex.artofproblemsolving.com/3/f/c/3fcf2348a3e59a7844a5a348039748c7d811fc78.png)
has 2 copies of the sequence inside it which are not disjoint.
probability of coming up heads and 
probability of coming up tails. The expected number of flips necessary to first see the sequence 
