and 
Prove that
Let 
and 
Prove that
prove that![\[ \frac{a^2}{b^2} + \frac{b^2}{c^2} + \frac{c^2}{d^2} + \frac{d^2}{a^2}\geq\frac{a}{d} + \frac{b}{a} + \frac{c}{b} + \frac{d}{c}\]](http://latex.artofproblemsolving.com/0/0/4/004e7f148bbb0c797688f5195aa4002dbc316470.png)
If you know same tasks, link them please
be the Fermat point of a 
.
,
,
are concurrent and the point of concurrence is 
,
(
well). i want to study so if you guys have some easy or normal problems please send me
Y by
You are given a positive integer 
. What is the largest possible number of numbers that can be chosen from the set
so that there are no two chosen numbers 
for which 
?
Here
denotes the greatest common divisor of 
.
Proposed by Anton Trygub
. What is the largest possible number of numbers that can be chosen from the set
so that there are no two chosen numbers 
for which 
?Here
denotes the greatest common divisor of 
.Proposed by Anton Trygub
.
such integers. Then, there must clearly be at least one pair of consecutive integers 
and 
.
,
