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.
![$P(x) \in \mathbb{R}[x]$](http://latex.artofproblemsolving.com/4/5/3/453a624c3b002c1b0e78e0023b24dd22ddd03557.png)
such that:
with 
is an 
th prime and 
is an arbitrary positive integer.
that verfy the following equation :
+1 w
+1 w
be a positive integer. We say that a positive integer 
is -good if 
is divisible by 
for all positive integers 
with 
. Suppose is a positive integer such that is -good, but 
is not -good. Prove that 
is prime.
let 
and 
be the circumcenter and the orthocenter. The point 
is the reflection of 
with respect to 
. Assume that is not on the same side of 
as . Points 
lie on 
respectively such that 
. Let 
be the intersection point of 
. Prove that 
a grid of 9*9, we choose a little square in of this grid three times, we can choose three times the same.
be the incenter of triangle 
. Let 
, 
, and 
be the orthocenters of triangles 
, 
, and 
, respectively. Prove that the lines through , , and , parallel to 
, 
, and 
, respectively, are concurrent.
,
.
is the inverse of function 
and thus, they might intersect that 
axis (if they do, we are done). Thus: 
is the only solution.
.
Let 
.
