AoPS Academy
+1 w
[/quote]
, do not answer with "
is a solution" only. Either you post any kind of proof or at least something unexpected (like "
is the smallest solution). Someone that does not see that is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
, where 
is a digit. How many pairs of such numbers are there such that their sum is also a palindrome?
, 
.
, such that 
and 
.
such that 
is prime, 
with 
and ?
be the incircle of 
. There are two smaller circles 
amd 
inside . The circle is tangent to at 
, tangent to 
at 
, and also tangent to 
. The circle is tangent to at 
, tangent to at 
, and also tangent to 
. Prove that 
are concyclic.
such that ![\[p^q+q^p+p+q-5pq\]](http://latex.artofproblemsolving.com/b/a/b/bab8a0ee3555cf1136b6de56179012b920d0a2ad.png)
is a perfect square.
with circumcircle 
, and two arbitrary points 
on . Let , , 
be points on lines , 
, , respectively, such that 
, 
, and 
concur at a point . Let 
be a point on line such that 
, 
, , are concyclic. Similarly, let 
be a point on line such that , , , are concyclic, and let 
be a point on line such that , , , are concyclic. Prove that 
, 
, 
concur at a single point.
be non-negative real numbers such that 
Prove that
is a triangle with incenter 
. The foot of the perpendicular from to is , and the foot of the perpendicular from to is . Prove that 
.
We will all miss him.
w![$ \boxed{\ \left(\frac{n}{n+1}\right)^{n+1}<\sqrt [n+1]{(n+1) !}-\sqrt [n]{n!}\ }$](http://latex.artofproblemsolving.com/d/f/2/df2545bd7a1f1759e55190e60648d5cf65a2488a.png)
be positive numbers such that 
.![\[T = \dfrac{bc}{\sqrt{a}+3}+\dfrac{ca}{\sqrt{b}+3}+\dfrac{ab}{\sqrt{c}+3} \]](http://latex.artofproblemsolving.com/6/d/5/6d570d06679f17452790b90171428d645e97fe9f.png)
Prove that 
