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, Mango247
Given a convex quadrilateral, is it always possible to determine a point, P, in it's interior such that the four line segments joining Point P to the midpoints of the sides divide the quadrilateral into four regions of equal area?
Follow Up: If such a point exists, is it unique?
Follow Up: If such a point exists, is it unique?
,
so that 
and 
so that 
( 
in my drawing), take 
midpoint of 
;
has the property 
.
;
