satisfying 
,![\[ \frac{a^4+5b^4}{a(a+2b)} + \frac{b^4+5c^4}{b(b+2c)} + \frac{c^4+5a^4}{c(c+2a)} \geq 1- ab-bc-ca \]](http://latex.artofproblemsolving.com/f/e/8/fe85cf52b883c214806ab837a2eb25cebb511d7b.png)
such that there exists a unique integer 
such that 
with the following property:![\[ n!\mid a^n + 1
\]](http://latex.artofproblemsolving.com/e/2/3/e23d39aab685888993d355d8c93d4e6475f53487.png)
(use in a problem for junior) to practice. Can anyone share to me?
Y by Adventure10, Mango247
Given three points 
, and 
in the plane construct a triangle such that its circumcenter is at 
, its incenter is at 
, and one of its excenters is at .
(B. Martynov)
, and 
in the plane construct a triangle such that its circumcenter is at 
, its incenter is at 
, and one of its excenters is at .(B. Martynov)
by 
.
.
to meet 
.
.
and 
.
.
