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
In a triangle 
, let 
be a point on the median 
such that 
. It turned out that 
. Show that 
.
, let 
be a point on the median 
such that 
. It turned out that 
. Show that 
.This post has been edited 1 time. Last edited by parmenides51, Sep 4, 2021, 3:50 PM
