be positive real numbers such that 
.![\[ \frac{a_{1} a_{2} \cdots a_{n} \left[ 1 - (a_{1} + a_{2} + \cdots + a_{n}) \right] }{(a_{1} + a_{2} + \cdots + a_{n})( 1 - a_{1})(1 - a_{2}) \cdots (1 - a_{n})} \leq \frac{1}{ n^{n+1}}. \]](http://latex.artofproblemsolving.com/6/5/5/65558feba82e32266d3d3cbdfea85e079483403f.png)
with integer coefficients such that for all positive number 
and prime 
satisfying 
,
.
be reals such that 
P
Y by Adventure10
Let there be a pentagon 
inscribed in a circle 
. The tangent to at 
is parallel to 
. A point 
lies on and it is in the opposite side of 
with respect to 
, and satisfies 
and 
. Prove that the tangent to at 
and line 
concur at one point.
inscribed in a circle 
. The tangent to at 
is parallel to 
. A point 
lies on and it is in the opposite side of 
with respect to 
, and satisfies 
and 
. Prove that the tangent to at 
and line 
concur at one point.
