AoPS Academy
[/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.
are exponential growth for 
and decay for 
still labelled growth although it's decreasing, or is there no label for it, or is it now classified as a decay (similar question for a function such as 
; still a decay, now a growth, or nothing?)
be a prime and suppose 
is prime. Prove that 
is prime
This is a special case of Pocklington's theorem. A proof of this special case is required.
be the circumcenter and 
the orthocenter of an acute triangle 
. Show that there exist points 
, 
, and 
on sides 
, 
, and 
respectively such that ![\[ OD + DH = OE + EH = OF + FH\]](http://latex.artofproblemsolving.com/a/8/7/a874af4cb802b9b341b055140a08e096aaf2112e.png)
and the lines 
, 
, and 
are concurrent.
such that: 
be an acute triangle with 
, and let and be points on side such that 
and lies between 
and . Suppose there exists a point 
inside such that 
and 
. Prove that 
.
numbers 
and 
numbers 
are written in some order.
.
, then jumps in some order on each of the numbers 
exactly once and finally returns with his last jump to . Can the total distance he travelled with these 
jumps be a) 
, b) 
?
satisfying the equation for all real numbers 
:![\[
f(x^2 + y + f(y)) = f(x)^2
\]](http://latex.artofproblemsolving.com/0/6/f/06f2c3b16aecf900a28c033c45993564afd80055.png)
then prove that 
.
