[/quote]
,
Prove that
Where 
Prove that
Let 
Prove that
Let 
Prove that
robots, each in a different cell.
and 
be prime numbers. Prove that if 
is a perfect square, then 
is also a perfect square.
in order to make it a perfect square?
,
When does the equality hold?
be the positive number satisfied 
Find the minimum of 
. Prove that
.
so that for any 
,![\[ f(xf(x^2)+yf(x))=xf(y+xf(x)). \]](http://latex.artofproblemsolving.com/1/d/4/1d4fbf3f80306aaae5cfc11cc0e4be7ea41491d7.png)
,
,
.
that are solutions of the equation 
.
![\[\frac{\sin^2A+\sin^2B+\sin^2C}{\cos^2A+\cos^2B+\cos^2C} = 2\]](http://latex.artofproblemsolving.com/9/2/a/92a524bbdca92e9dd4091275714bf346bad96cd7.png)
Y by TDVOLIMPTEAM
While I was thinking on some other geometry problem, a NT problem came to my mind. Despite some tries(which were mostly order), I could not find a way to solve the problem. As I searched, this problem has never been posted before. Here is the problem.
Find all positive integers
such that:
Moreover, I wonder if there is a way to solve the question in this variant:
Find all positive integers
such that:
Find all positive integers
such that:
Moreover, I wonder if there is a way to solve the question in this variant:
Find all positive integers
such that:
where 
.
.
.
