with no obtuse angles.![$$\frac1{\sqrt3}\cdot\left(\cot A+\cot B+\cot C\right)+\left(2-\sqrt 3\right)\sqrt[3]{\cot A\cot B\cot C}\geq\frac2{\sqrt3}.$$](http://latex.artofproblemsolving.com/d/1/4/d14154281d7ccf60a2dcfe1d937b974ae1d74f97.png)
,
and 
lie on 
and 
respectively such that 
.
and 
are the reflections of 
lies on segment 
such that the circumcenter of triangle 
coincides with the circumcenter of triangle 
.
such that : 
such that : 
Y by
Prove that for all positive integers 
, 
is a perfect square.
, 
is a perfect square.This post has been edited 3 times. Last edited by jl_, Apr 23, 2025, 10:22 AM
Reason: Change subject and source
Reason: Change subject and source
.
