![\[ \frac{a}{\sqrt{a^2 + 8bc}} + \frac{b}{\sqrt{b^2 + 8ca}} + \frac{c}{\sqrt{c^2 + 8ab}} \geq 1. \]](http://latex.artofproblemsolving.com/b/2/f/b2ff456632d4dd3b9ed93e4cba437bdd34d54cd8.png)
,
,
cut three common chords concurrent at 
.
,
which are internally tangent to all 
.
be a parallelogram of center 
.
,
and 
such that 
.
Y by
Find all positive integers 
such that there exists a monic polynomial 
of degree with integers coefficients satisfying
for all integers 
.
such that there exists a monic polynomial 
of degree with integers coefficients satisfying
for all integers 
.This post has been edited 5 times. Last edited by Quidditch, Jun 16, 2022, 3:11 AM
,
So, this case clearly fails.
,
So, this case also fails.
